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Polynomial regression

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3339: 2328: 3334:{\displaystyle {\begin{bmatrix}\sum _{i=1}^{n}x_{i}^{0}&\sum _{i=1}^{n}x_{i}^{1}&\sum _{i=1}^{n}x_{i}^{2}&\cdots &\sum _{i=1}^{n}x_{i}^{m}\\\sum _{i=1}^{n}x_{i}^{1}&\sum _{i=1}^{n}x_{i}^{2}&\sum _{i=1}^{n}x_{i}^{3}&\cdots &\sum _{i=1}^{n}x_{i}^{m+1}\\\sum _{i=1}^{n}x_{i}^{2}&\sum _{i=1}^{n}x_{i}^{3}&\sum _{i=1}^{n}x_{i}^{4}&\cdots &\sum _{i=1}^{n}x_{i}^{m+2}\\\vdots &\vdots &\vdots &\ddots &\vdots \\\sum _{i=1}^{n}x_{i}^{m}&\sum _{i=1}^{n}x_{i}^{m+1}&\sum _{i=1}^{n}x_{i}^{m+2}&\dots &\sum _{i=1}^{n}x_{i}^{2m}\\\end{bmatrix}}{\begin{bmatrix}\beta _{0}\\\beta _{1}\\\beta _{2}\\\cdots \\\beta _{m}\\\end{bmatrix}}={\begin{bmatrix}\sum _{i=1}^{n}y_{i}x_{i}^{0}\\\sum _{i=1}^{n}y_{i}x_{i}^{1}\\\sum _{i=1}^{n}y_{i}x_{i}^{2}\\\cdots \\\sum _{i=1}^{n}y_{i}x_{i}^{m}\\\end{bmatrix}}} 2056: 3686: 1539: 3394: 2051:{\displaystyle {\begin{bmatrix}y_{1}\\y_{2}\\y_{3}\\\vdots \\y_{n}\end{bmatrix}}={\begin{bmatrix}1&x_{1}&x_{1}^{2}&\dots &x_{1}^{m}\\1&x_{2}&x_{2}^{2}&\dots &x_{2}^{m}\\1&x_{3}&x_{3}^{2}&\dots &x_{3}^{m}\\\vdots &\vdots &\vdots &\ddots &\vdots \\1&x_{n}&x_{n}^{2}&\dots &x_{n}^{m}\end{bmatrix}}{\begin{bmatrix}\beta _{0}\\\beta _{1}\\\beta _{2}\\\vdots \\\beta _{m}\end{bmatrix}}+{\begin{bmatrix}\varepsilon _{1}\\\varepsilon _{2}\\\varepsilon _{3}\\\vdots \\\varepsilon _{n}\end{bmatrix}},} 3681:{\displaystyle {\begin{aligned}&\qquad {\widehat {y}}=\beta _{0}x^{0}+\beta _{1}x^{1}+\beta _{2}x^{2}+\cdots +\beta _{m}x^{m}\\&\qquad \\&\qquad {\text{Where:}}\\&\qquad n={\text{number of }}x_{i}y_{i}{\text{ variable pairs in the data}}\\&\qquad m={\text{order of the polynomial to be used for regression}}\\&\qquad \beta _{(0-m)}={\text{polynomial coefficient for each corresponding }}x^{(0-m)}\\&\qquad {\widehat {y}}={\text{estimated y variable based on the polynomial regression calculations.}}\end{aligned}}} 7311: 6704: 405: 6690: 609: 6728: 6716: 2322:
The above matrix equations explain the behavior of polynomial regression well. However, to physically implement polynomial regression for a set of xy point pairs, more detail is useful. The below matrix equations for polynomial coefficients are expanded from regression theory without derivation and
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In many settings, such a linear relationship may not hold. For example, if we are modeling the yield of a chemical synthesis in terms of the temperature at which the synthesis takes place, we may find that the yield improves by increasing amounts for each unit increase in temperature. In this case,
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Although polynomial regression is technically a special case of multiple linear regression, the interpretation of a fitted polynomial regression model requires a somewhat different perspective. It is often difficult to interpret the individual coefficients in a polynomial regression fit, since the
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can be useful alternatives to polynomial regression. Some of these methods make use of a localized form of classical polynomial regression. An advantage of traditional polynomial regression is that the inferential framework of multiple regression can be used (this also holds when using other
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The goal of polynomial regression is to model a non-linear relationship between the independent and dependent variables (technically, between the independent variable and the conditional mean of the dependent variable). This is similar to the goal of
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The explanatory (independent) variables resulting from the polynomial expansion of the "baseline" variables are known as higher-degree terms. Such variables are also used in
2281: 1486: 1373: 1515: 1402: 2312: 6828: 6752: 5825: 600:. More recently, the use of polynomial models has been complemented by other methods, with non-polynomial models having advantages for some classes of problems. 6330: 4370:. Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104). p. 259. 6480: 6104: 6837: 4745: 4027: 2067: 6842: 5878: 435: 6317: 7275: 345: 730: 4375: 4348: 7170: 6810: 4740: 4440: 4102: 335: 5344: 4492: 6732: 1343:{\displaystyle y_{i}\,=\,\beta _{0}+\beta _{1}x_{i}+\beta _{2}x_{i}^{2}+\cdots +\beta _{m}x_{i}^{m}+\varepsilon _{i}\ (i=1,2,\dots ,n)} 7150: 6800: 3824: 7070: 6127: 6019: 4279: 3705: 1151:
analysis, the computational and inferential problems of polynomial regression can be completely addressed using the techniques of
6876: 6305: 6179: 2243:{\displaystyle {\widehat {\vec {\beta }}}=(\mathbf {X} ^{\mathsf {T}}\mathbf {X} )^{-1}\;\mathbf {X} ^{\mathsf {T}}{\vec {y}},\,} 299: 3773: 6363: 6024: 5769: 5140: 4730: 350: 288: 108: 83: 5354: 638: 7112: 6414: 5626: 5433: 5322: 5280: 210: 4519: 3350: 6657: 5616: 169: 5666: 7363: 7298: 7198: 7188: 7107: 7052: 6208: 6157: 6142: 6132: 6001: 5873: 5840: 5621: 5451: 4037: 428: 6277: 5578: 7325: 7140: 6552: 6353: 5332: 5001: 4465: 4022: 3712:, it is generally more informative to consider the fitted regression function as a whole. Point-wise or simultaneous 371: 6437: 6404: 3968:, which aims to capture non-linear regression relationships. Therefore, non-parametric regression approaches such as 6820: 6409: 6152: 5911: 5817: 5797: 5705: 5416: 5234: 4717: 4589: 3344: 1530: 538: 531: 340: 309: 236: 5583: 5349: 5207: 4054:
Microsoft Excel makes use of polynomial regression when fitting a trendline to data points on an X Y scatter plot.
823: 7165: 6992: 6956: 6925: 6169: 5937: 5658: 5512: 5441: 5361: 5219: 5200: 4908: 4629: 3981: 330: 319: 283: 190: 7145: 6282: 4071: 1119:{\displaystyle y=\beta _{0}+\beta _{1}x+\beta _{2}x^{2}+\beta _{3}x^{3}+\cdots +\beta _{n}x^{n}+\varepsilon .\,} 565: 391: 7023: 6987: 6915: 6805: 6787: 6652: 6419: 5967: 5932: 5896: 5681: 5123: 5032: 4991: 4903: 4594: 4433: 4032: 3965: 3918:. A drawback of polynomial bases is that the basis functions are "non-local", meaning that the fitted value of 3731: 262: 185: 78: 57: 5689: 5673: 920: 6886: 6561: 6174: 6114: 6051: 5411: 5273: 5263: 5113: 5027: 491: 421: 314: 6322: 6259: 1436: 7239: 7065: 6930: 6920: 6871: 6599: 6529: 6014: 5901: 4898: 4795: 4702: 4581: 4480: 4158:(November 1974). "Gergonne's 1815 paper on the design and analysis of polynomial regression experiments". 4000: 3992: 3709: 2136: 278: 273: 215: 6720: 5598: 617: 7320: 7280: 7244: 7229: 7180: 7124: 6624: 6566: 6509: 6335: 6228: 6137: 5863: 5747: 5606: 5488: 5480: 5295: 5191: 5169: 5128: 5093: 5060: 5006: 4981: 4936: 4875: 4835: 4637: 4460: 4298:
that are not constant (everywhere). Such "non-local" behavior has been widely discussed in statistics:
3953: 597: 593: 581: 569: 366: 7310: 6703: 5593: 404: 4124:(November 1974) . "The application of the method of least squares to the interpolation of sequences". 7285: 7224: 7211: 7160: 7060: 6982: 6961: 6935: 6547: 6122: 6071: 6047: 6009: 5927: 5906: 5858: 5737: 5715: 5684: 5470: 5421: 5339: 5312: 5268: 5224: 4986: 4762: 4642: 4269: 4121: 3949: 1407: 698: 585: 558: 461: 386: 376: 257: 225: 180: 159: 67: 7303: 7234: 7119: 7086: 7038: 7028: 7007: 7002: 6881: 6863: 6848: 6779: 6694: 6619: 6542: 6223: 5987: 5980: 5942: 5850: 5830: 5802: 5535: 5401: 5396: 5386: 5378: 5196: 5157: 5047: 5037: 4946: 4725: 4681: 4599: 4524: 4426: 3716:
can then be used to provide a sense of the uncertainty in the estimate of the regression function.
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Local Polynomial Modelling and Its Applications: From linear regression to nonlinear regression
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to model a functional relationship between two quantities. More specifically, it replaces
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The goal of regression analysis is to model the expected value of a dependent variable
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in terms of the value of an independent variable (or vector of independent variables)
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Yin-Wen Chang; Cho-Jui Hsieh; Kai-Wei Chang; Michael Ringgaard; Chih-Jen Lin (2010).
4012: 1148: 898: 550: 252: 128: 4815: 6604: 6537: 6514: 6429: 5759: 5055: 4953: 4888: 4830: 4752: 4707: 1163:, ... as being distinct independent variables in a multiple regression model. 118: 4250: 6853: 6647: 6609: 6292: 6193: 6055: 5868: 5835: 5327: 5244: 5239: 4883: 4840: 4820: 4800: 4790: 4559: 530:. For this reason, polynomial regression is considered to be a special case of 164: 113: 3708:
on the interval (0, 1). Although the correlation can be reduced by using
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is used, where Îľ is an unobserved random error with mean zero conditioned on a
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nonlinear even though the model is linear in the parameters to be estimated.
5646: 5498: 5118: 4913: 4825: 4810: 4805: 4770: 4343:. Monographs on Statistics and Applied Probability. Chapman & Hall/CRC. 3969: 523: 3944:. In modern statistics, polynomial basis-functions are used along with new 486:. Polynomial regression fits a nonlinear relationship between the value of 5162: 4780: 4657: 4652: 4647: 4619: 4098:"Training and testing low-degree polynomial data mappings via linear SVM" 554: 802:{\displaystyle y=\beta _{0}+\beta _{1}x+\beta _{2}x^{2}+\varepsilon .\,} 6667: 6368: 4323: 4210: 3957: 989:
th degree polynomial, yielding the general polynomial regression model
4274:(4th ed.). US: Brooks/Cole Publishing Company. pp. 539–542. 6589: 5570: 5544: 5524: 4775: 4566: 4302:
Magee, Lonnie (1998). "Nonlocal Behavior in Polynomial Regressions".
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estimated y variable based on the polynomial regression calculations.
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Conveniently, these models are all linear from the point of view of
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Polynomial regression is one example of regression analysis using
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The vector of estimated polynomial regression coefficients (using
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problem it is linear, in the sense that the regression function E(
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Polynomial regression models are usually fit using the method of
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values are distinct. This is the unique least-squares solution.
527: 6748: 6478: 6045: 5792: 5091: 4861: 4478: 4422: 3911:{\displaystyle {\mathbin {\stackrel {\varphi }{\rightarrow }}}} 2287:, the invertibility condition is guaranteed to hold if all the 612:
A cubic polynomial regression fit to a simulated data set. The
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which is required for the matrix to be invertible; then since
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underlying monomials can be highly correlated. For example,
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can be expressed in matrix form in terms of a design matrix
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is a 95% simultaneous confidence band constructed using the
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Probability and Statistics for Engineering and the Sciences
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Interactive simulations, University of Colorado at Boulder
3814:{\displaystyle \varphi (x)\in \mathbb {R} ^{d_{\varphi }}} 705:. In this model, for each unit increase in the value of 687:{\displaystyle y=\beta _{0}+\beta _{1}x+\varepsilon ,\,} 584:
for polynomial regression appeared in an 1815 paper of
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Elementary Numerical Analysis: An Algorithmic Approach
3382:{\displaystyle \beta _{0}{\text{ through }}\beta _{m}} 3117: 3039: 2337: 1975: 1897: 1626: 1548: 812:
In this model, when the temperature is increased from
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Autoregressive conditional heteroskedasticity (ARCH)
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which when using pure matrix notation is written as
1529:-th data sample. Then the model can be written as a 820: + 1 units, the expected yield changes by 568:. The least-squares method was published in 1805 by 7258: 7207: 7179: 7133: 7079: 7051: 7016: 6975: 6944: 6906: 6895: 6862: 6819: 6786: 6638: 6575: 6528: 6491: 6446: 6428: 6395: 6386: 6344: 6291: 6252: 6201: 6192: 6113: 6070: 6000: 5966: 5920: 5887: 5849: 5816: 5728: 5637: 5556: 5511: 5479: 5432: 5377: 5303: 5294: 5104: 5046: 5020: 4972: 4927: 4874: 4761: 4716: 4690: 4672: 4628: 4580: 4500: 4491: 4226:"Maths behind Polynomial regression, Muthukrishnan" 3623:
polynomial coefficient for each corresponding 
3910: 3813: 3762: 3680: 3381: 3333: 2306: 2275: 2242: 2124: 2050: 1509: 1480: 1454: 1425: 1396: 1367: 1342: 1118: 958: 873: 801: 686: 3587:order of the polynomial to be used for regression 564:of the coefficients, under the conditions of the 5879:Multivariate adaptive regression splines (MARS) 981:In general, we can model the expected value of 724:we might propose a quadratic model of the form 3973:families of basis functions such as splines). 6760: 4434: 4255:Polynomial Regression, A PHP regression class 966:The fact that the change in yield depends on 429: 8: 874:{\displaystyle \beta _{1}+\beta _{2}(2x+1).} 4294:Such "non-local" behavior is a property of 4003:estimator may be used to account for that. 3770:in linear regression with polynomial basis 6903: 6767: 6753: 6745: 6488: 6475: 6392: 6198: 6067: 6042: 5813: 5789: 5517: 5300: 5101: 5088: 4871: 4858: 4497: 4488: 4475: 4441: 4427: 4419: 4399:"Tutorial: Polynomial Regression in Excel" 2209: 632:. In simple linear regression, the model 436: 422: 29: 4136:from the 1815 French ed.): 439–447. 4072:"Implementation of Polynomial Regression" 4028:Polynomial and rational function modeling 3899: 3880: 3852: 3847: 3845: 3844: 3843: 3826: 3803: 3798: 3794: 3793: 3775: 3763:{\displaystyle x\in \mathbb {R} ^{d_{x}}} 3752: 3747: 3743: 3742: 3733: 3669: 3655: 3654: 3630: 3621: 3600: 3585: 3568: 3562: 3552: 3543: 3526: 3508: 3498: 3479: 3469: 3456: 3446: 3433: 3423: 3405: 3404: 3398: 3396: 3373: 3364: 3358: 3352: 3317: 3312: 3302: 3292: 3281: 3260: 3255: 3245: 3235: 3224: 3210: 3205: 3195: 3185: 3174: 3160: 3155: 3145: 3135: 3124: 3112: 3095: 3074: 3060: 3046: 3034: 3017: 3012: 3002: 2991: 2968: 2963: 2953: 2942: 2924: 2919: 2909: 2898: 2886: 2881: 2871: 2860: 2813: 2808: 2798: 2787: 2770: 2765: 2755: 2744: 2732: 2727: 2717: 2706: 2694: 2689: 2679: 2668: 2648: 2643: 2633: 2622: 2605: 2600: 2590: 2579: 2567: 2562: 2552: 2541: 2529: 2524: 2514: 2503: 2489: 2484: 2474: 2463: 2446: 2441: 2431: 2420: 2408: 2403: 2393: 2382: 2370: 2365: 2355: 2344: 2332: 2330: 2298: 2292: 2268: 2266: 2239: 2225: 2224: 2217: 2216: 2211: 2200: 2191: 2184: 2183: 2178: 2155: 2153: 2152: 2150: 2121: 2107: 2106: 2092: 2091: 2086: 2072: 2071: 2069: 2031: 2010: 1996: 1982: 1970: 1953: 1932: 1918: 1904: 1892: 1878: 1873: 1856: 1851: 1839: 1793: 1788: 1771: 1766: 1754: 1735: 1730: 1713: 1708: 1696: 1677: 1672: 1655: 1650: 1638: 1621: 1604: 1583: 1569: 1555: 1543: 1541: 1496: 1495: 1493: 1473: 1471: 1441: 1440: 1438: 1412: 1411: 1409: 1383: 1382: 1380: 1360: 1358: 1298: 1285: 1280: 1270: 1251: 1246: 1236: 1223: 1213: 1200: 1195: 1191: 1185: 1179: 1115: 1100: 1090: 1071: 1061: 1048: 1038: 1022: 1009: 997: 944: 928: 922: 844: 831: 825: 798: 783: 773: 757: 744: 732: 683: 665: 652: 640: 553:. The least-squares method minimizes the 510:fits a nonlinear model to the data, as a 1167:Matrix form and calculation of estimates 959:{\displaystyle \beta _{1}+2\beta _{2}x.} 607: 7276:Numerical smoothing and differentiation 4063: 3704:have correlation around 0.97 when x is 970:is what makes the relationship between 592:, with a greater emphasis on issues of 358: 244: 44: 37: 6405:Kaplan–Meier estimator (product limit) 4251:"Mathematics of Polynomial Regression" 4132:(4) (Translated by Ralph St. John and 2218: 2185: 460:in which the relationship between the 3933:depends strongly on data values with 1455:{\displaystyle {\vec {\varepsilon }}} 7: 6811:Iteratively reweighted least squares 6715: 6415:Accelerated failure time (AFT) model 4224:Muthukrishnan, Gowri (17 Jun 2018). 4103:Journal of Machine Learning Research 6727: 6010:Analysis of variance (ANOVA, anova) 889:+1 and subtracting the equation in 6829:Pearson product-moment correlation 6105:Cochran–Mantel–Haenszel statistics 4731:Pearson product-moment correlation 4230:Maths behind Polynomial regression 25: 4364:Conte, S.D.; De Boor, C. (2018). 709:, the conditional expectation of 7309: 6726: 6714: 6702: 6689: 6688: 3570: variable pairs in the data 2269: 2212: 2192: 2179: 2087: 1474: 1361: 1171:The polynomial regression model 403: 6364:Least-squares spectral analysis 3653: 3595: 3578: 3536: 3525: 3519: 3403: 1426:{\displaystyle {\vec {\beta }}} 881:(This can be seen by replacing 351:Least-squares spectral analysis 289:Generalized estimating equation 109:Multinomial logistic regression 84:Vector generalized linear model 5345:Mean-unbiased minimum-variance 3976:A final alternative is to use 3905: 3861: 3848: 3840: 3828: 3786: 3780: 3643: 3631: 3613: 3601: 2230: 2197: 2174: 2160: 2112: 2097: 2077: 1501: 1446: 1417: 1388: 1337: 1307: 865: 850: 1: 6658:Geographic information system 5874:Simultaneous equations models 170:Nonlinear mixed-effects model 7299:Regression analysis category 7189:Response surface methodology 5841:Coefficient of determination 5452:Uniformly most powerful test 4172:10.1016/0315-0860(74)90033-0 4142:10.1016/0315-0860(74)90034-2 4038:Response surface methodology 2276:{\displaystyle \mathbf {X} } 1481:{\displaystyle \mathbf {X} } 1368:{\displaystyle \mathbf {X} } 1155:. This is done by treating 1147:, .... Therefore, for 526:that are estimated from the 7171:Frisch–Waugh–Lovell theorem 7141:Mean and predicted response 6410:Proportional hazards models 6354:Spectral density estimation 6336:Vector autoregression (VAR) 5770:Maximum posterior estimator 5002:Randomized controlled trial 4023:Local polynomial regression 522:) is linear in the unknown 372:Mean and predicted response 7380: 6821:Correlation and dependence 6170:Multivariate distributions 4590:Average absolute deviation 3345:system of linear equations 1531:system of linear equations 1510:{\displaystyle {\vec {y}}} 1397:{\displaystyle {\vec {y}}} 566:Gauss–Markov theorem 532:multiple linear regression 165:Linear mixed-effects model 7294: 7166:Minimum mean-square error 7053:Decomposition of variance 6957:Growth curve (statistics) 6926:Generalized least squares 6684: 6487: 6474: 6158:Structural equation model 6066: 6041: 5812: 5788: 5520: 5494:Score/Lagrange multiplier 5100: 5087: 4909:Sample size determination 4870: 4857: 4487: 4474: 4456: 4403:facultystaff.richmond.edu 4304:The American Statistician 3982:support vector regression 331:Least absolute deviations 7024:Generalized linear model 6916:Simple linear regression 6806:Non-linear least squares 6788:Computational statistics 6653:Environmental statistics 6175:Elliptical distributions 5968:Generalized linear model 5897:Simple linear regression 5667:Hodges–Lehmann estimator 5124:Probability distribution 5033:Stochastic approximation 4595:Coefficient of variation 4397:Stevenson, Christopher. 4185:Smith, Kirstine (1918). 4033:Polynomial interpolation 3966:nonparametric regression 3343:After solving the above 79:Generalized linear model 18:Polynomial least squares 6313:Cross-correlation (XCF) 5921:Non-standard predictors 5355:Lehmann–ScheffĂŠ theorem 5028:Adaptive clinical trial 4268:Devore, Jay L. (1995). 7316:Mathematics portal 7240:Orthogonal polynomials 7066:Analysis of covariance 6931:Weighted least squares 6921:Ordinary least squares 6872:Ordinary least squares 6709:Mathematics portal 6530:Engineering statistics 6438:Nelson–Aalen estimator 6015:Analysis of covariance 5902:Ordinary least squares 5826:Pearson product-moment 5230:Statistical functional 5141:Empirical distribution 4974:Controlled experiments 4703:Frequency distribution 4481:Descriptive statistics 4339:Fan, Jianqing (1996). 4001:weighted least squares 3954:radial basis functions 3912: 3815: 3764: 3720:Alternative approaches 3710:orthogonal polynomials 3682: 3383: 3335: 3297: 3240: 3190: 3140: 3007: 2958: 2914: 2876: 2803: 2760: 2722: 2684: 2638: 2595: 2557: 2519: 2479: 2436: 2398: 2360: 2308: 2277: 2244: 2137:ordinary least squares 2126: 2052: 1511: 1482: 1462:of random errors. The 1456: 1427: 1398: 1369: 1344: 1120: 960: 885:in this equation with 875: 803: 688: 621: 604:Definition and example 512:statistical estimation 490:and the corresponding 410:Mathematics portal 336:Iteratively reweighted 7281:System identification 7245:Chebyshev polynomials 7230:Numerical integration 7181:Design of experiments 7125:Regression validation 6952:Polynomial regression 6877:Partial least squares 6625:Population statistics 6567:System identification 6301:Autocorrelation (ACF) 6229:Exponential smoothing 6143:Discriminant analysis 6138:Canonical correlation 6002:Partition of variance 5864:Regression validation 5708:(Jonckheere–Terpstra) 5607:Likelihood-ratio test 5296:Frequentist inference 5208:Location–scale family 5129:Sampling distribution 5094:Statistical inference 5061:Cross-sectional study 5048:Observational studies 5007:Randomized experiment 4836:Stem-and-leaf display 4638:Central limit theorem 3913: 3816: 3765: 3706:uniformly distributed 3683: 3384: 3336: 3277: 3220: 3170: 3120: 2987: 2938: 2894: 2856: 2783: 2740: 2702: 2664: 2618: 2575: 2537: 2499: 2459: 2416: 2378: 2340: 2309: 2307:{\displaystyle x_{i}} 2278: 2245: 2127: 2053: 1512: 1483: 1457: 1428: 1404:, a parameter vector 1399: 1370: 1345: 1121: 961: 893:from the equation in 876: 804: 689: 611: 508:polynomial regression 454:polynomial regression 367:Regression validation 346:Bayesian multivariate 63:Polynomial regression 7286:Moving least squares 7225:Approximation theory 7161:Studentized residual 7151:Errors and residuals 7146:Gauss–Markov theorem 7061:Analysis of variance 6983:Nonlinear regression 6962:Segmented regression 6936:General linear model 6854:Confounding variable 6801:Linear least squares 6548:Probabilistic design 6133:Principal components 5976:Exponential families 5928:Nonlinear regression 5907:General linear model 5869:Mixed effects models 5859:Errors and residuals 5836:Confounding variable 5738:Bayesian probability 5716:Van der Waerden test 5706:Ordered alternative 5471:Multiple comparisons 5350:Rao–Blackwellization 5313:Estimating equations 5269:Statistical distance 4987:Factorial experiment 4520:Arithmetic-Geometric 4160:Historia Mathematica 4126:Historia Mathematica 3825: 3774: 3732: 3395: 3351: 2329: 2323:easily implemented. 2291: 2265: 2149: 2068: 1540: 1492: 1470: 1437: 1408: 1379: 1375:, a response vector 1357: 1178: 996: 921: 824: 731: 639: 462:independent variable 392:Gauss–Markov theorem 387:Studentized residual 377:Errors and residuals 211:Principal components 181:Nonlinear regression 68:General linear model 7364:Regression analysis 7304:Statistics category 7235:Gaussian quadrature 7120:Model specification 7087:Stepwise regression 6945:Predictor structure 6882:Total least squares 6864:Regression analysis 6849:Partial correlation 6780:regression analysis 6620:Official statistics 6543:Methods engineering 6224:Seasonal adjustment 5992:Poisson regressions 5912:Bayesian regression 5851:Regression analysis 5831:Partial correlation 5803:Regression analysis 5402:Prediction interval 5397:Likelihood interval 5387:Confidence interval 5379:Interval estimation 5340:Unbiased estimators 5158:Model specification 5038:Up-and-down designs 4726:Partial correlation 4682:Index of dispersion 4600:Interquartile range 4156:Stigler, Stephen M. 3366: through  3322: 3265: 3215: 3165: 3025: 2979: 2935: 2891: 2824: 2775: 2737: 2699: 2659: 2610: 2572: 2534: 2494: 2451: 2413: 2375: 1883: 1861: 1798: 1776: 1740: 1718: 1682: 1660: 1290: 1256: 1153:multiple regression 590:regression analysis 458:regression analysis 237:Errors-in-variables 104:Logistic regression 94:Binomial regression 39:Regression analysis 33:Part of a series on 7321:Statistics outline 7220:Numerical analysis 6640:Spatial statistics 6520:Medical statistics 6420:First hitting time 6374:Whittle likelihood 6025:Degrees of freedom 6020:Multivariate ANOVA 5953:Heteroscedasticity 5765:Bayesian estimator 5730:Bayesian inference 5579:Kolmogorov–Smirnov 5464:Randomization test 5434:Testing hypotheses 5407:Tolerance interval 5318:Maximum likelihood 5213:Exponential family 5146:Density estimation 5106:Statistical theory 5066:Natural experiment 5012:Scientific control 4929:Survey methodology 4615:Standard deviation 4296:analytic functions 3908: 3811: 3760: 3678: 3676: 3379: 3331: 3325: 3308: 3251: 3201: 3151: 3103: 3028: 3008: 2959: 2915: 2877: 2804: 2761: 2723: 2685: 2639: 2596: 2558: 2520: 2480: 2437: 2399: 2361: 2304: 2285:Vandermonde matrix 2273: 2240: 2122: 2048: 2039: 1961: 1886: 1869: 1847: 1784: 1762: 1726: 1704: 1668: 1646: 1612: 1507: 1478: 1452: 1423: 1394: 1365: 1340: 1276: 1242: 1116: 956: 871: 799: 684: 622: 469:dependent variable 124:Multinomial probit 27:Statistics concept 7334: 7333: 7326:Statistics topics 7271:Calibration curve 7080:Model exploration 7047: 7046: 7017:Non-normal errors 6908:Linear regression 6899:statistical model 6742: 6741: 6680: 6679: 6676: 6675: 6615:National accounts 6585:Actuarial science 6577:Social statistics 6470: 6469: 6466: 6465: 6462: 6461: 6397:Survival function 6382: 6381: 6244:Granger causality 6085:Contingency table 6060:Survival analysis 6037: 6036: 6033: 6032: 5889:Linear regression 5784: 5783: 5780: 5779: 5755:Credible interval 5724: 5723: 5507: 5506: 5323:Method of moments 5192:Parametric family 5153:Statistical model 5083: 5082: 5079: 5078: 4997:Random assignment 4919:Statistical power 4853: 4852: 4849: 4848: 4698:Contingency table 4668: 4667: 4535:Generalized/power 4377:978-1-61197-520-8 4350:978-0-412-98321-4 3986:polynomial kernel 3922:at a given value 3857: 3672: 3663: 3624: 3588: 3571: 3546: 3529: 3413: 3367: 2318:Expanded formulas 2233: 2168: 2163: 2115: 2100: 2080: 1517:will contain the 1504: 1449: 1420: 1391: 1306: 474:is modeled as an 446: 445: 99:Binary regression 58:Simple regression 53:Linear regression 16:(Redirected from 7371: 7314: 7313: 7071:Multivariate AOV 6967:Local regression 6904: 6896:Regression as a 6887:Ridge regression 6834:Rank correlation 6769: 6762: 6755: 6746: 6730: 6729: 6718: 6717: 6707: 6706: 6692: 6691: 6595:Crime statistics 6489: 6476: 6393: 6359:Fourier analysis 6346:Frequency domain 6326: 6273: 6239:Structural break 6199: 6148:Cluster analysis 6095:Log-linear model 6068: 6043: 5984: 5958:Homoscedasticity 5814: 5790: 5709: 5701: 5693: 5692:(Kruskal–Wallis) 5677: 5662: 5617:Cross validation 5602: 5584:Anderson–Darling 5531: 5518: 5489:Likelihood-ratio 5481:Parametric tests 5459:Permutation test 5442:1- & 2-tails 5333:Minimum distance 5305:Point estimation 5301: 5252:Optimal decision 5203: 5102: 5089: 5071:Quasi-experiment 5021:Adaptive designs 4872: 4859: 4736:Rank correlation 4498: 4489: 4476: 4443: 4436: 4429: 4420: 4414: 4413: 4411: 4409: 4394: 4388: 4387: 4385: 4384: 4361: 4355: 4354: 4336: 4330: 4327: 4292: 4286: 4285: 4265: 4259: 4258: 4247: 4241: 4240: 4238: 4236: 4221: 4215: 4214: 4182: 4176: 4175: 4152: 4146: 4145: 4118: 4112: 4111: 4093: 4087: 4086: 4084: 4083: 4068: 4043:Smoothing spline 3997:unequal variance 3917: 3915: 3914: 3909: 3904: 3903: 3885: 3884: 3860: 3859: 3858: 3856: 3851: 3846: 3820: 3818: 3817: 3812: 3810: 3809: 3808: 3807: 3797: 3769: 3767: 3766: 3761: 3759: 3758: 3757: 3756: 3746: 3714:confidence bands 3687: 3685: 3684: 3679: 3677: 3673: 3670: 3665: 3664: 3656: 3651: 3647: 3646: 3625: 3622: 3617: 3616: 3593: 3589: 3586: 3576: 3572: 3569: 3567: 3566: 3557: 3556: 3547: 3544: 3534: 3530: 3527: 3523: 3517: 3513: 3512: 3503: 3502: 3484: 3483: 3474: 3473: 3461: 3460: 3451: 3450: 3438: 3437: 3428: 3427: 3415: 3414: 3406: 3401: 3388: 3386: 3385: 3380: 3378: 3377: 3368: 3365: 3363: 3362: 3340: 3338: 3337: 3332: 3330: 3329: 3321: 3316: 3307: 3306: 3296: 3291: 3264: 3259: 3250: 3249: 3239: 3234: 3214: 3209: 3200: 3199: 3189: 3184: 3164: 3159: 3150: 3149: 3139: 3134: 3108: 3107: 3100: 3099: 3079: 3078: 3065: 3064: 3051: 3050: 3033: 3032: 3024: 3016: 3006: 3001: 2978: 2967: 2957: 2952: 2934: 2923: 2913: 2908: 2890: 2885: 2875: 2870: 2823: 2812: 2802: 2797: 2774: 2769: 2759: 2754: 2736: 2731: 2721: 2716: 2698: 2693: 2683: 2678: 2658: 2647: 2637: 2632: 2609: 2604: 2594: 2589: 2571: 2566: 2556: 2551: 2533: 2528: 2518: 2513: 2493: 2488: 2478: 2473: 2450: 2445: 2435: 2430: 2412: 2407: 2397: 2392: 2374: 2369: 2359: 2354: 2313: 2311: 2310: 2305: 2303: 2302: 2282: 2280: 2279: 2274: 2272: 2249: 2247: 2246: 2241: 2235: 2234: 2226: 2223: 2222: 2221: 2215: 2208: 2207: 2195: 2190: 2189: 2188: 2182: 2170: 2169: 2164: 2156: 2154: 2131: 2129: 2128: 2123: 2117: 2116: 2108: 2102: 2101: 2093: 2090: 2082: 2081: 2073: 2057: 2055: 2054: 2049: 2044: 2043: 2036: 2035: 2015: 2014: 2001: 2000: 1987: 1986: 1966: 1965: 1958: 1957: 1937: 1936: 1923: 1922: 1909: 1908: 1891: 1890: 1882: 1877: 1860: 1855: 1844: 1843: 1797: 1792: 1775: 1770: 1759: 1758: 1739: 1734: 1717: 1712: 1701: 1700: 1681: 1676: 1659: 1654: 1643: 1642: 1617: 1616: 1609: 1608: 1588: 1587: 1574: 1573: 1560: 1559: 1516: 1514: 1513: 1508: 1506: 1505: 1497: 1487: 1485: 1484: 1479: 1477: 1461: 1459: 1458: 1453: 1451: 1450: 1442: 1432: 1430: 1429: 1424: 1422: 1421: 1413: 1403: 1401: 1400: 1395: 1393: 1392: 1384: 1374: 1372: 1371: 1366: 1364: 1349: 1347: 1346: 1341: 1304: 1303: 1302: 1289: 1284: 1275: 1274: 1255: 1250: 1241: 1240: 1228: 1227: 1218: 1217: 1205: 1204: 1190: 1189: 1125: 1123: 1122: 1117: 1105: 1104: 1095: 1094: 1076: 1075: 1066: 1065: 1053: 1052: 1043: 1042: 1027: 1026: 1014: 1013: 965: 963: 962: 957: 949: 948: 933: 932: 913:with respect to 911:total derivative 909:is given by the 905:, the effect on 880: 878: 877: 872: 849: 848: 836: 835: 808: 806: 805: 800: 788: 787: 778: 777: 762: 761: 749: 748: 693: 691: 690: 685: 670: 669: 657: 656: 492:conditional mean 438: 431: 424: 408: 407: 315:Ridge regression 150:Multilevel model 30: 21: 7379: 7378: 7374: 7373: 7372: 7370: 7369: 7368: 7354: 7353: 7340: 7335: 7330: 7308: 7290: 7254: 7250:Chebyshev nodes 7203: 7199:Bayesian design 7175: 7156:Goodness of fit 7129: 7102: 7092:Model selection 7075: 7043: 7012: 6971: 6940: 6897: 6891: 6858: 6815: 6782: 6773: 6743: 6738: 6701: 6672: 6634: 6571: 6557:quality control 6524: 6506:Clinical trials 6483: 6458: 6442: 6430:Hazard function 6424: 6378: 6340: 6324: 6287: 6283:Breusch–Godfrey 6271: 6248: 6188: 6163:Factor analysis 6109: 6090:Graphical model 6062: 6029: 5996: 5982: 5962: 5916: 5883: 5845: 5808: 5807: 5776: 5720: 5707: 5699: 5691: 5675: 5660: 5639:Rank statistics 5633: 5612:Model selection 5600: 5558:Goodness of fit 5552: 5529: 5503: 5475: 5428: 5373: 5362:Median unbiased 5290: 5201: 5134:Order statistic 5096: 5075: 5042: 5016: 4968: 4923: 4866: 4864:Data collection 4845: 4757: 4712: 4686: 4664: 4624: 4576: 4493:Continuous data 4483: 4470: 4452: 4447: 4417: 4407: 4405: 4396: 4395: 4391: 4382: 4380: 4378: 4363: 4362: 4358: 4351: 4338: 4337: 4333: 4316:10.2307/2685560 4301: 4293: 4289: 4282: 4267: 4266: 4262: 4249: 4248: 4244: 4234: 4232: 4223: 4222: 4218: 4203:10.2307/2331929 4184: 4183: 4179: 4154: 4153: 4149: 4122:Gergonne, J. D. 4120: 4119: 4115: 4095: 4094: 4090: 4081: 4079: 4070: 4069: 4065: 4061: 4051: 4018:Line regression 4009: 3980:models such as 3946:basis functions 3943: 3932: 3895: 3876: 3823: 3822: 3799: 3792: 3772: 3771: 3748: 3741: 3730: 3729: 3726:basis functions 3722: 3693: 3675: 3674: 3649: 3648: 3626: 3596: 3591: 3590: 3574: 3573: 3558: 3548: 3545:number of  3532: 3531: 3521: 3520: 3515: 3514: 3504: 3494: 3475: 3465: 3452: 3442: 3429: 3419: 3393: 3392: 3369: 3354: 3349: 3348: 3324: 3323: 3298: 3274: 3273: 3267: 3266: 3241: 3217: 3216: 3191: 3167: 3166: 3141: 3113: 3102: 3101: 3091: 3088: 3087: 3081: 3080: 3070: 3067: 3066: 3056: 3053: 3052: 3042: 3035: 3027: 3026: 2985: 2980: 2936: 2892: 2853: 2852: 2847: 2842: 2837: 2832: 2826: 2825: 2781: 2776: 2738: 2700: 2661: 2660: 2616: 2611: 2573: 2535: 2496: 2495: 2457: 2452: 2414: 2376: 2333: 2327: 2326: 2320: 2294: 2289: 2288: 2263: 2262: 2210: 2196: 2177: 2147: 2146: 2066: 2065: 2038: 2037: 2027: 2024: 2023: 2017: 2016: 2006: 2003: 2002: 1992: 1989: 1988: 1978: 1971: 1960: 1959: 1949: 1946: 1945: 1939: 1938: 1928: 1925: 1924: 1914: 1911: 1910: 1900: 1893: 1885: 1884: 1867: 1862: 1845: 1835: 1833: 1827: 1826: 1821: 1816: 1811: 1806: 1800: 1799: 1782: 1777: 1760: 1750: 1748: 1742: 1741: 1724: 1719: 1702: 1692: 1690: 1684: 1683: 1666: 1661: 1644: 1634: 1632: 1622: 1611: 1610: 1600: 1597: 1596: 1590: 1589: 1579: 1576: 1575: 1565: 1562: 1561: 1551: 1544: 1538: 1537: 1490: 1489: 1468: 1467: 1435: 1434: 1433:, and a vector 1406: 1405: 1377: 1376: 1355: 1354: 1294: 1266: 1232: 1219: 1209: 1196: 1181: 1176: 1175: 1169: 1146: 1139: 1096: 1086: 1067: 1057: 1044: 1034: 1018: 1005: 994: 993: 940: 924: 919: 918: 840: 827: 822: 821: 779: 769: 753: 740: 729: 728: 719: 661: 648: 637: 636: 614:confidence band 606: 572:and in 1809 by 547: 442: 402: 382:Goodness of fit 89:Discrete choice 28: 23: 22: 15: 12: 11: 5: 7377: 7375: 7367: 7366: 7356: 7355: 7352: 7351: 7339: 7338:External links 7336: 7332: 7331: 7329: 7328: 7323: 7318: 7306: 7301: 7295: 7292: 7291: 7289: 7288: 7283: 7278: 7273: 7268: 7262: 7260: 7256: 7255: 7253: 7252: 7247: 7242: 7237: 7232: 7227: 7222: 7216: 7214: 7205: 7204: 7202: 7201: 7196: 7194:Optimal design 7191: 7185: 7183: 7177: 7176: 7174: 7173: 7168: 7163: 7158: 7153: 7148: 7143: 7137: 7135: 7131: 7130: 7128: 7127: 7122: 7117: 7116: 7115: 7110: 7105: 7100: 7089: 7083: 7081: 7077: 7076: 7074: 7073: 7068: 7063: 7057: 7055: 7049: 7048: 7045: 7044: 7042: 7041: 7036: 7031: 7026: 7020: 7018: 7014: 7013: 7011: 7010: 7005: 7000: 6995: 6993:Semiparametric 6990: 6985: 6979: 6977: 6973: 6972: 6970: 6969: 6964: 6959: 6954: 6948: 6946: 6942: 6941: 6939: 6938: 6933: 6928: 6923: 6918: 6912: 6910: 6901: 6893: 6892: 6890: 6889: 6884: 6879: 6874: 6868: 6866: 6860: 6859: 6857: 6856: 6851: 6846: 6840: 6838:Spearman's rho 6831: 6825: 6823: 6817: 6816: 6814: 6813: 6808: 6803: 6798: 6792: 6790: 6784: 6783: 6774: 6772: 6771: 6764: 6757: 6749: 6740: 6739: 6737: 6736: 6724: 6712: 6698: 6685: 6682: 6681: 6678: 6677: 6674: 6673: 6671: 6670: 6665: 6660: 6655: 6650: 6644: 6642: 6636: 6635: 6633: 6632: 6627: 6622: 6617: 6612: 6607: 6602: 6597: 6592: 6587: 6581: 6579: 6573: 6572: 6570: 6569: 6564: 6559: 6550: 6545: 6540: 6534: 6532: 6526: 6525: 6523: 6522: 6517: 6512: 6503: 6501:Bioinformatics 6497: 6495: 6485: 6484: 6479: 6472: 6471: 6468: 6467: 6464: 6463: 6460: 6459: 6457: 6456: 6450: 6448: 6444: 6443: 6441: 6440: 6434: 6432: 6426: 6425: 6423: 6422: 6417: 6412: 6407: 6401: 6399: 6390: 6384: 6383: 6380: 6379: 6377: 6376: 6371: 6366: 6361: 6356: 6350: 6348: 6342: 6341: 6339: 6338: 6333: 6328: 6320: 6315: 6310: 6309: 6308: 6306:partial (PACF) 6297: 6295: 6289: 6288: 6286: 6285: 6280: 6275: 6267: 6262: 6256: 6254: 6253:Specific tests 6250: 6249: 6247: 6246: 6241: 6236: 6231: 6226: 6221: 6216: 6211: 6205: 6203: 6196: 6190: 6189: 6187: 6186: 6185: 6184: 6183: 6182: 6167: 6166: 6165: 6155: 6153:Classification 6150: 6145: 6140: 6135: 6130: 6125: 6119: 6117: 6111: 6110: 6108: 6107: 6102: 6100:McNemar's test 6097: 6092: 6087: 6082: 6076: 6074: 6064: 6063: 6046: 6039: 6038: 6035: 6034: 6031: 6030: 6028: 6027: 6022: 6017: 6012: 6006: 6004: 5998: 5997: 5995: 5994: 5978: 5972: 5970: 5964: 5963: 5961: 5960: 5955: 5950: 5945: 5940: 5938:Semiparametric 5935: 5930: 5924: 5922: 5918: 5917: 5915: 5914: 5909: 5904: 5899: 5893: 5891: 5885: 5884: 5882: 5881: 5876: 5871: 5866: 5861: 5855: 5853: 5847: 5846: 5844: 5843: 5838: 5833: 5828: 5822: 5820: 5810: 5809: 5806: 5805: 5800: 5794: 5793: 5786: 5785: 5782: 5781: 5778: 5777: 5775: 5774: 5773: 5772: 5762: 5757: 5752: 5751: 5750: 5745: 5734: 5732: 5726: 5725: 5722: 5721: 5719: 5718: 5713: 5712: 5711: 5703: 5695: 5679: 5676:(Mann–Whitney) 5671: 5670: 5669: 5656: 5655: 5654: 5643: 5641: 5635: 5634: 5632: 5631: 5630: 5629: 5624: 5619: 5609: 5604: 5601:(Shapiro–Wilk) 5596: 5591: 5586: 5581: 5576: 5568: 5562: 5560: 5554: 5553: 5551: 5550: 5542: 5533: 5521: 5515: 5513:Specific tests 5509: 5508: 5505: 5504: 5502: 5501: 5496: 5491: 5485: 5483: 5477: 5476: 5474: 5473: 5468: 5467: 5466: 5456: 5455: 5454: 5444: 5438: 5436: 5430: 5429: 5427: 5426: 5425: 5424: 5419: 5409: 5404: 5399: 5394: 5389: 5383: 5381: 5375: 5374: 5372: 5371: 5366: 5365: 5364: 5359: 5358: 5357: 5352: 5337: 5336: 5335: 5330: 5325: 5320: 5309: 5307: 5298: 5292: 5291: 5289: 5288: 5283: 5278: 5277: 5276: 5266: 5261: 5260: 5259: 5249: 5248: 5247: 5242: 5237: 5227: 5222: 5217: 5216: 5215: 5210: 5205: 5189: 5188: 5187: 5182: 5177: 5167: 5166: 5165: 5160: 5150: 5149: 5148: 5138: 5137: 5136: 5126: 5121: 5116: 5110: 5108: 5098: 5097: 5092: 5085: 5084: 5081: 5080: 5077: 5076: 5074: 5073: 5068: 5063: 5058: 5052: 5050: 5044: 5043: 5041: 5040: 5035: 5030: 5024: 5022: 5018: 5017: 5015: 5014: 5009: 5004: 4999: 4994: 4989: 4984: 4978: 4976: 4970: 4969: 4967: 4966: 4964:Standard error 4961: 4956: 4951: 4950: 4949: 4944: 4933: 4931: 4925: 4924: 4922: 4921: 4916: 4911: 4906: 4901: 4896: 4894:Optimal design 4891: 4886: 4880: 4878: 4868: 4867: 4862: 4855: 4854: 4851: 4850: 4847: 4846: 4844: 4843: 4838: 4833: 4828: 4823: 4818: 4813: 4808: 4803: 4798: 4793: 4788: 4783: 4778: 4773: 4767: 4765: 4759: 4758: 4756: 4755: 4750: 4749: 4748: 4743: 4733: 4728: 4722: 4720: 4714: 4713: 4711: 4710: 4705: 4700: 4694: 4692: 4691:Summary tables 4688: 4687: 4685: 4684: 4678: 4676: 4670: 4669: 4666: 4665: 4663: 4662: 4661: 4660: 4655: 4650: 4640: 4634: 4632: 4626: 4625: 4623: 4622: 4617: 4612: 4607: 4602: 4597: 4592: 4586: 4584: 4578: 4577: 4575: 4574: 4569: 4564: 4563: 4562: 4557: 4552: 4547: 4542: 4537: 4532: 4527: 4525:Contraharmonic 4522: 4517: 4506: 4504: 4495: 4485: 4484: 4479: 4472: 4471: 4469: 4468: 4463: 4457: 4454: 4453: 4448: 4446: 4445: 4438: 4431: 4423: 4416: 4415: 4389: 4376: 4356: 4349: 4331: 4329: 4328: 4287: 4280: 4260: 4242: 4216: 4177: 4166:(4): 431–439. 4147: 4113: 4088: 4062: 4060: 4057: 4056: 4055: 4050: 4047: 4046: 4045: 4040: 4035: 4030: 4025: 4020: 4015: 4008: 4005: 3941: 3930: 3907: 3902: 3898: 3894: 3891: 3888: 3883: 3879: 3875: 3872: 3869: 3866: 3863: 3855: 3850: 3842: 3839: 3836: 3833: 3830: 3806: 3802: 3796: 3791: 3788: 3785: 3782: 3779: 3755: 3751: 3745: 3740: 3737: 3721: 3718: 3692: 3691:Interpretation 3689: 3668: 3662: 3659: 3652: 3650: 3645: 3642: 3639: 3636: 3633: 3629: 3620: 3615: 3612: 3609: 3606: 3603: 3599: 3594: 3592: 3584: 3581: 3577: 3575: 3565: 3561: 3555: 3551: 3542: 3539: 3535: 3533: 3524: 3522: 3518: 3516: 3511: 3507: 3501: 3497: 3493: 3490: 3487: 3482: 3478: 3472: 3468: 3464: 3459: 3455: 3449: 3445: 3441: 3436: 3432: 3426: 3422: 3418: 3412: 3409: 3402: 3400: 3376: 3372: 3361: 3357: 3328: 3320: 3315: 3311: 3305: 3301: 3295: 3290: 3287: 3284: 3280: 3276: 3275: 3272: 3269: 3268: 3263: 3258: 3254: 3248: 3244: 3238: 3233: 3230: 3227: 3223: 3219: 3218: 3213: 3208: 3204: 3198: 3194: 3188: 3183: 3180: 3177: 3173: 3169: 3168: 3163: 3158: 3154: 3148: 3144: 3138: 3133: 3130: 3127: 3123: 3119: 3118: 3116: 3111: 3106: 3098: 3094: 3090: 3089: 3086: 3083: 3082: 3077: 3073: 3069: 3068: 3063: 3059: 3055: 3054: 3049: 3045: 3041: 3040: 3038: 3031: 3023: 3020: 3015: 3011: 3005: 3000: 2997: 2994: 2990: 2986: 2984: 2981: 2977: 2974: 2971: 2966: 2962: 2956: 2951: 2948: 2945: 2941: 2937: 2933: 2930: 2927: 2922: 2918: 2912: 2907: 2904: 2901: 2897: 2893: 2889: 2884: 2880: 2874: 2869: 2866: 2863: 2859: 2855: 2854: 2851: 2848: 2846: 2843: 2841: 2838: 2836: 2833: 2831: 2828: 2827: 2822: 2819: 2816: 2811: 2807: 2801: 2796: 2793: 2790: 2786: 2782: 2780: 2777: 2773: 2768: 2764: 2758: 2753: 2750: 2747: 2743: 2739: 2735: 2730: 2726: 2720: 2715: 2712: 2709: 2705: 2701: 2697: 2692: 2688: 2682: 2677: 2674: 2671: 2667: 2663: 2662: 2657: 2654: 2651: 2646: 2642: 2636: 2631: 2628: 2625: 2621: 2617: 2615: 2612: 2608: 2603: 2599: 2593: 2588: 2585: 2582: 2578: 2574: 2570: 2565: 2561: 2555: 2550: 2547: 2544: 2540: 2536: 2532: 2527: 2523: 2517: 2512: 2509: 2506: 2502: 2498: 2497: 2492: 2487: 2483: 2477: 2472: 2469: 2466: 2462: 2458: 2456: 2453: 2449: 2444: 2440: 2434: 2429: 2426: 2423: 2419: 2415: 2411: 2406: 2402: 2396: 2391: 2388: 2385: 2381: 2377: 2373: 2368: 2364: 2358: 2353: 2350: 2347: 2343: 2339: 2338: 2336: 2319: 2316: 2301: 2297: 2271: 2251: 2250: 2238: 2232: 2229: 2220: 2214: 2206: 2203: 2199: 2194: 2187: 2181: 2176: 2173: 2167: 2162: 2159: 2133: 2132: 2120: 2114: 2111: 2105: 2099: 2096: 2089: 2085: 2079: 2076: 2059: 2058: 2047: 2042: 2034: 2030: 2026: 2025: 2022: 2019: 2018: 2013: 2009: 2005: 2004: 1999: 1995: 1991: 1990: 1985: 1981: 1977: 1976: 1974: 1969: 1964: 1956: 1952: 1948: 1947: 1944: 1941: 1940: 1935: 1931: 1927: 1926: 1921: 1917: 1913: 1912: 1907: 1903: 1899: 1898: 1896: 1889: 1881: 1876: 1872: 1868: 1866: 1863: 1859: 1854: 1850: 1846: 1842: 1838: 1834: 1832: 1829: 1828: 1825: 1822: 1820: 1817: 1815: 1812: 1810: 1807: 1805: 1802: 1801: 1796: 1791: 1787: 1783: 1781: 1778: 1774: 1769: 1765: 1761: 1757: 1753: 1749: 1747: 1744: 1743: 1738: 1733: 1729: 1725: 1723: 1720: 1716: 1711: 1707: 1703: 1699: 1695: 1691: 1689: 1686: 1685: 1680: 1675: 1671: 1667: 1665: 1662: 1658: 1653: 1649: 1645: 1641: 1637: 1633: 1631: 1628: 1627: 1625: 1620: 1615: 1607: 1603: 1599: 1598: 1595: 1592: 1591: 1586: 1582: 1578: 1577: 1572: 1568: 1564: 1563: 1558: 1554: 1550: 1549: 1547: 1525:value for the 1503: 1500: 1476: 1448: 1445: 1419: 1416: 1390: 1387: 1363: 1351: 1350: 1339: 1336: 1333: 1330: 1327: 1324: 1321: 1318: 1315: 1312: 1309: 1301: 1297: 1293: 1288: 1283: 1279: 1273: 1269: 1265: 1262: 1259: 1254: 1249: 1245: 1239: 1235: 1231: 1226: 1222: 1216: 1212: 1208: 1203: 1199: 1194: 1188: 1184: 1168: 1165: 1144: 1137: 1127: 1126: 1114: 1111: 1108: 1103: 1099: 1093: 1089: 1085: 1082: 1079: 1074: 1070: 1064: 1060: 1056: 1051: 1047: 1041: 1037: 1033: 1030: 1025: 1021: 1017: 1012: 1008: 1004: 1001: 955: 952: 947: 943: 939: 936: 931: 927: 870: 867: 864: 861: 858: 855: 852: 847: 843: 839: 834: 830: 810: 809: 797: 794: 791: 786: 782: 776: 772: 768: 765: 760: 756: 752: 747: 743: 739: 736: 717: 695: 694: 682: 679: 676: 673: 668: 664: 660: 655: 651: 647: 644: 605: 602: 546: 543: 539:classification 444: 443: 441: 440: 433: 426: 418: 415: 414: 413: 412: 397: 396: 395: 394: 389: 384: 379: 374: 369: 361: 360: 356: 355: 354: 353: 348: 343: 338: 333: 325: 324: 323: 322: 317: 312: 307: 302: 294: 293: 292: 291: 286: 281: 276: 268: 267: 266: 265: 260: 255: 247: 246: 242: 241: 240: 239: 231: 230: 229: 228: 223: 218: 213: 208: 203: 198: 193: 191:Semiparametric 188: 183: 175: 174: 173: 172: 167: 162: 160:Random effects 157: 152: 144: 143: 142: 141: 136: 134:Ordered probit 131: 126: 121: 116: 111: 106: 101: 96: 91: 86: 81: 73: 72: 71: 70: 65: 60: 55: 47: 46: 42: 41: 35: 34: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 7376: 7365: 7362: 7361: 7359: 7349: 7345: 7344:Curve Fitting 7342: 7341: 7337: 7327: 7324: 7322: 7319: 7317: 7312: 7307: 7305: 7302: 7300: 7297: 7296: 7293: 7287: 7284: 7282: 7279: 7277: 7274: 7272: 7269: 7267: 7266:Curve fitting 7264: 7263: 7261: 7257: 7251: 7248: 7246: 7243: 7241: 7238: 7236: 7233: 7231: 7228: 7226: 7223: 7221: 7218: 7217: 7215: 7213: 7212:approximation 7210: 7206: 7200: 7197: 7195: 7192: 7190: 7187: 7186: 7184: 7182: 7178: 7172: 7169: 7167: 7164: 7162: 7159: 7157: 7154: 7152: 7149: 7147: 7144: 7142: 7139: 7138: 7136: 7132: 7126: 7123: 7121: 7118: 7114: 7111: 7109: 7106: 7104: 7103: 7095: 7094: 7093: 7090: 7088: 7085: 7084: 7082: 7078: 7072: 7069: 7067: 7064: 7062: 7059: 7058: 7056: 7054: 7050: 7040: 7037: 7035: 7032: 7030: 7027: 7025: 7022: 7021: 7019: 7015: 7009: 7006: 7004: 7001: 6999: 6996: 6994: 6991: 6989: 6988:Nonparametric 6986: 6984: 6981: 6980: 6978: 6974: 6968: 6965: 6963: 6960: 6958: 6955: 6953: 6950: 6949: 6947: 6943: 6937: 6934: 6932: 6929: 6927: 6924: 6922: 6919: 6917: 6914: 6913: 6911: 6909: 6905: 6902: 6900: 6894: 6888: 6885: 6883: 6880: 6878: 6875: 6873: 6870: 6869: 6867: 6865: 6861: 6855: 6852: 6850: 6847: 6844: 6843:Kendall's tau 6841: 6839: 6835: 6832: 6830: 6827: 6826: 6824: 6822: 6818: 6812: 6809: 6807: 6804: 6802: 6799: 6797: 6796:Least squares 6794: 6793: 6791: 6789: 6785: 6781: 6777: 6776:Least squares 6770: 6765: 6763: 6758: 6756: 6751: 6750: 6747: 6735: 6734: 6725: 6723: 6722: 6713: 6711: 6710: 6705: 6699: 6697: 6696: 6687: 6686: 6683: 6669: 6666: 6664: 6663:Geostatistics 6661: 6659: 6656: 6654: 6651: 6649: 6646: 6645: 6643: 6641: 6637: 6631: 6630:Psychometrics 6628: 6626: 6623: 6621: 6618: 6616: 6613: 6611: 6608: 6606: 6603: 6601: 6598: 6596: 6593: 6591: 6588: 6586: 6583: 6582: 6580: 6578: 6574: 6568: 6565: 6563: 6560: 6558: 6554: 6551: 6549: 6546: 6544: 6541: 6539: 6536: 6535: 6533: 6531: 6527: 6521: 6518: 6516: 6513: 6511: 6507: 6504: 6502: 6499: 6498: 6496: 6494: 6493:Biostatistics 6490: 6486: 6482: 6477: 6473: 6455: 6454:Log-rank test 6452: 6451: 6449: 6445: 6439: 6436: 6435: 6433: 6431: 6427: 6421: 6418: 6416: 6413: 6411: 6408: 6406: 6403: 6402: 6400: 6398: 6394: 6391: 6389: 6385: 6375: 6372: 6370: 6367: 6365: 6362: 6360: 6357: 6355: 6352: 6351: 6349: 6347: 6343: 6337: 6334: 6332: 6329: 6327: 6325:(Box–Jenkins) 6321: 6319: 6316: 6314: 6311: 6307: 6304: 6303: 6302: 6299: 6298: 6296: 6294: 6290: 6284: 6281: 6279: 6278:Durbin–Watson 6276: 6274: 6268: 6266: 6263: 6261: 6260:Dickey–Fuller 6258: 6257: 6255: 6251: 6245: 6242: 6240: 6237: 6235: 6234:Cointegration 6232: 6230: 6227: 6225: 6222: 6220: 6217: 6215: 6212: 6210: 6209:Decomposition 6207: 6206: 6204: 6200: 6197: 6195: 6191: 6181: 6178: 6177: 6176: 6173: 6172: 6171: 6168: 6164: 6161: 6160: 6159: 6156: 6154: 6151: 6149: 6146: 6144: 6141: 6139: 6136: 6134: 6131: 6129: 6126: 6124: 6121: 6120: 6118: 6116: 6112: 6106: 6103: 6101: 6098: 6096: 6093: 6091: 6088: 6086: 6083: 6081: 6080:Cohen's kappa 6078: 6077: 6075: 6073: 6069: 6065: 6061: 6057: 6053: 6049: 6044: 6040: 6026: 6023: 6021: 6018: 6016: 6013: 6011: 6008: 6007: 6005: 6003: 5999: 5993: 5989: 5985: 5979: 5977: 5974: 5973: 5971: 5969: 5965: 5959: 5956: 5954: 5951: 5949: 5946: 5944: 5941: 5939: 5936: 5934: 5933:Nonparametric 5931: 5929: 5926: 5925: 5923: 5919: 5913: 5910: 5908: 5905: 5903: 5900: 5898: 5895: 5894: 5892: 5890: 5886: 5880: 5877: 5875: 5872: 5870: 5867: 5865: 5862: 5860: 5857: 5856: 5854: 5852: 5848: 5842: 5839: 5837: 5834: 5832: 5829: 5827: 5824: 5823: 5821: 5819: 5815: 5811: 5804: 5801: 5799: 5796: 5795: 5791: 5787: 5771: 5768: 5767: 5766: 5763: 5761: 5758: 5756: 5753: 5749: 5746: 5744: 5741: 5740: 5739: 5736: 5735: 5733: 5731: 5727: 5717: 5714: 5710: 5704: 5702: 5696: 5694: 5688: 5687: 5686: 5683: 5682:Nonparametric 5680: 5678: 5672: 5668: 5665: 5664: 5663: 5657: 5653: 5652:Sample median 5650: 5649: 5648: 5645: 5644: 5642: 5640: 5636: 5628: 5625: 5623: 5620: 5618: 5615: 5614: 5613: 5610: 5608: 5605: 5603: 5597: 5595: 5592: 5590: 5587: 5585: 5582: 5580: 5577: 5575: 5573: 5569: 5567: 5564: 5563: 5561: 5559: 5555: 5549: 5547: 5543: 5541: 5539: 5534: 5532: 5527: 5523: 5522: 5519: 5516: 5514: 5510: 5500: 5497: 5495: 5492: 5490: 5487: 5486: 5484: 5482: 5478: 5472: 5469: 5465: 5462: 5461: 5460: 5457: 5453: 5450: 5449: 5448: 5445: 5443: 5440: 5439: 5437: 5435: 5431: 5423: 5420: 5418: 5415: 5414: 5413: 5410: 5408: 5405: 5403: 5400: 5398: 5395: 5393: 5390: 5388: 5385: 5384: 5382: 5380: 5376: 5370: 5367: 5363: 5360: 5356: 5353: 5351: 5348: 5347: 5346: 5343: 5342: 5341: 5338: 5334: 5331: 5329: 5326: 5324: 5321: 5319: 5316: 5315: 5314: 5311: 5310: 5308: 5306: 5302: 5299: 5297: 5293: 5287: 5284: 5282: 5279: 5275: 5272: 5271: 5270: 5267: 5265: 5262: 5258: 5257:loss function 5255: 5254: 5253: 5250: 5246: 5243: 5241: 5238: 5236: 5233: 5232: 5231: 5228: 5226: 5223: 5221: 5218: 5214: 5211: 5209: 5206: 5204: 5198: 5195: 5194: 5193: 5190: 5186: 5183: 5181: 5178: 5176: 5173: 5172: 5171: 5168: 5164: 5161: 5159: 5156: 5155: 5154: 5151: 5147: 5144: 5143: 5142: 5139: 5135: 5132: 5131: 5130: 5127: 5125: 5122: 5120: 5117: 5115: 5112: 5111: 5109: 5107: 5103: 5099: 5095: 5090: 5086: 5072: 5069: 5067: 5064: 5062: 5059: 5057: 5054: 5053: 5051: 5049: 5045: 5039: 5036: 5034: 5031: 5029: 5026: 5025: 5023: 5019: 5013: 5010: 5008: 5005: 5003: 5000: 4998: 4995: 4993: 4990: 4988: 4985: 4983: 4980: 4979: 4977: 4975: 4971: 4965: 4962: 4960: 4959:Questionnaire 4957: 4955: 4952: 4948: 4945: 4943: 4940: 4939: 4938: 4935: 4934: 4932: 4930: 4926: 4920: 4917: 4915: 4912: 4910: 4907: 4905: 4902: 4900: 4897: 4895: 4892: 4890: 4887: 4885: 4882: 4881: 4879: 4877: 4873: 4869: 4865: 4860: 4856: 4842: 4839: 4837: 4834: 4832: 4829: 4827: 4824: 4822: 4819: 4817: 4814: 4812: 4809: 4807: 4804: 4802: 4799: 4797: 4794: 4792: 4789: 4787: 4786:Control chart 4784: 4782: 4779: 4777: 4774: 4772: 4769: 4768: 4766: 4764: 4760: 4754: 4751: 4747: 4744: 4742: 4739: 4738: 4737: 4734: 4732: 4729: 4727: 4724: 4723: 4721: 4719: 4715: 4709: 4706: 4704: 4701: 4699: 4696: 4695: 4693: 4689: 4683: 4680: 4679: 4677: 4675: 4671: 4659: 4656: 4654: 4651: 4649: 4646: 4645: 4644: 4641: 4639: 4636: 4635: 4633: 4631: 4627: 4621: 4618: 4616: 4613: 4611: 4608: 4606: 4603: 4601: 4598: 4596: 4593: 4591: 4588: 4587: 4585: 4583: 4579: 4573: 4570: 4568: 4565: 4561: 4558: 4556: 4553: 4551: 4548: 4546: 4543: 4541: 4538: 4536: 4533: 4531: 4528: 4526: 4523: 4521: 4518: 4516: 4513: 4512: 4511: 4508: 4507: 4505: 4503: 4499: 4496: 4494: 4490: 4486: 4482: 4477: 4473: 4467: 4464: 4462: 4459: 4458: 4455: 4451: 4444: 4439: 4437: 4432: 4430: 4425: 4424: 4421: 4404: 4400: 4393: 4390: 4379: 4373: 4369: 4368: 4360: 4357: 4352: 4346: 4342: 4335: 4332: 4325: 4321: 4317: 4313: 4309: 4305: 4300: 4299: 4297: 4291: 4288: 4283: 4281:0-534-24264-2 4277: 4273: 4272: 4264: 4261: 4256: 4252: 4246: 4243: 4231: 4227: 4220: 4217: 4212: 4208: 4204: 4200: 4197:(1/2): 1–85. 4196: 4192: 4188: 4181: 4178: 4173: 4169: 4165: 4161: 4157: 4151: 4148: 4143: 4139: 4135: 4134:S. M. Stigler 4131: 4127: 4123: 4117: 4114: 4109: 4105: 4104: 4099: 4092: 4089: 4077: 4076:GeeksforGeeks 4073: 4067: 4064: 4058: 4053: 4052: 4048: 4044: 4041: 4039: 4036: 4034: 4031: 4029: 4026: 4024: 4021: 4019: 4016: 4014: 4013:Curve fitting 4011: 4010: 4006: 4004: 4002: 3998: 3994: 3989: 3987: 3983: 3979: 3974: 3971: 3967: 3961: 3959: 3955: 3951: 3947: 3940: 3936: 3929: 3926: =  3925: 3921: 3900: 3896: 3892: 3889: 3886: 3881: 3877: 3873: 3870: 3867: 3864: 3853: 3837: 3834: 3831: 3804: 3800: 3789: 3783: 3777: 3753: 3749: 3738: 3735: 3727: 3719: 3717: 3715: 3711: 3707: 3703: 3699: 3690: 3688: 3666: 3660: 3657: 3640: 3637: 3634: 3627: 3618: 3610: 3607: 3604: 3597: 3582: 3579: 3563: 3559: 3553: 3549: 3540: 3537: 3509: 3505: 3499: 3495: 3491: 3488: 3485: 3480: 3476: 3470: 3466: 3462: 3457: 3453: 3447: 3443: 3439: 3434: 3430: 3424: 3420: 3416: 3410: 3407: 3390: 3374: 3370: 3359: 3355: 3346: 3341: 3326: 3318: 3313: 3309: 3303: 3299: 3293: 3288: 3285: 3282: 3278: 3270: 3261: 3256: 3252: 3246: 3242: 3236: 3231: 3228: 3225: 3221: 3211: 3206: 3202: 3196: 3192: 3186: 3181: 3178: 3175: 3171: 3161: 3156: 3152: 3146: 3142: 3136: 3131: 3128: 3125: 3121: 3114: 3109: 3104: 3096: 3092: 3084: 3075: 3071: 3061: 3057: 3047: 3043: 3036: 3029: 3021: 3018: 3013: 3009: 3003: 2998: 2995: 2992: 2988: 2982: 2975: 2972: 2969: 2964: 2960: 2954: 2949: 2946: 2943: 2939: 2931: 2928: 2925: 2920: 2916: 2910: 2905: 2902: 2899: 2895: 2887: 2882: 2878: 2872: 2867: 2864: 2861: 2857: 2849: 2844: 2839: 2834: 2829: 2820: 2817: 2814: 2809: 2805: 2799: 2794: 2791: 2788: 2784: 2778: 2771: 2766: 2762: 2756: 2751: 2748: 2745: 2741: 2733: 2728: 2724: 2718: 2713: 2710: 2707: 2703: 2695: 2690: 2686: 2680: 2675: 2672: 2669: 2665: 2655: 2652: 2649: 2644: 2640: 2634: 2629: 2626: 2623: 2619: 2613: 2606: 2601: 2597: 2591: 2586: 2583: 2580: 2576: 2568: 2563: 2559: 2553: 2548: 2545: 2542: 2538: 2530: 2525: 2521: 2515: 2510: 2507: 2504: 2500: 2490: 2485: 2481: 2475: 2470: 2467: 2464: 2460: 2454: 2447: 2442: 2438: 2432: 2427: 2424: 2421: 2417: 2409: 2404: 2400: 2394: 2389: 2386: 2383: 2379: 2371: 2366: 2362: 2356: 2351: 2348: 2345: 2341: 2334: 2324: 2317: 2315: 2299: 2295: 2286: 2260: 2256: 2236: 2227: 2204: 2201: 2171: 2165: 2157: 2145: 2144: 2143: 2141: 2138: 2118: 2109: 2103: 2094: 2083: 2074: 2064: 2063: 2062: 2045: 2040: 2032: 2028: 2020: 2011: 2007: 1997: 1993: 1983: 1979: 1972: 1967: 1962: 1954: 1950: 1942: 1933: 1929: 1919: 1915: 1905: 1901: 1894: 1887: 1879: 1874: 1870: 1864: 1857: 1852: 1848: 1840: 1836: 1830: 1823: 1818: 1813: 1808: 1803: 1794: 1789: 1785: 1779: 1772: 1767: 1763: 1755: 1751: 1745: 1736: 1731: 1727: 1721: 1714: 1709: 1705: 1697: 1693: 1687: 1678: 1673: 1669: 1663: 1656: 1651: 1647: 1639: 1635: 1629: 1623: 1618: 1613: 1605: 1601: 1593: 1584: 1580: 1570: 1566: 1556: 1552: 1545: 1536: 1535: 1534: 1532: 1528: 1524: 1520: 1498: 1465: 1443: 1414: 1385: 1334: 1331: 1328: 1325: 1322: 1319: 1316: 1313: 1310: 1299: 1295: 1291: 1286: 1281: 1277: 1271: 1267: 1263: 1260: 1257: 1252: 1247: 1243: 1237: 1233: 1229: 1224: 1220: 1214: 1210: 1206: 1201: 1197: 1192: 1186: 1182: 1174: 1173: 1172: 1166: 1164: 1162: 1158: 1154: 1150: 1149:least squares 1143: 1136: 1132: 1112: 1109: 1106: 1101: 1097: 1091: 1087: 1083: 1080: 1077: 1072: 1068: 1062: 1058: 1054: 1049: 1045: 1039: 1035: 1031: 1028: 1023: 1019: 1015: 1010: 1006: 1002: 999: 992: 991: 990: 988: 984: 979: 977: 973: 969: 953: 950: 945: 941: 937: 934: 929: 925: 916: 912: 908: 904: 900: 899:infinitesimal 896: 892: 888: 884: 868: 862: 859: 856: 853: 845: 841: 837: 832: 828: 819: 815: 795: 792: 789: 784: 780: 774: 770: 766: 763: 758: 754: 750: 745: 741: 737: 734: 727: 726: 725: 721: 716: 713:increases by 712: 708: 704: 700: 680: 677: 674: 671: 666: 662: 658: 653: 649: 645: 642: 635: 634: 633: 631: 627: 619: 615: 610: 603: 601: 599: 595: 591: 587: 583: 579: 575: 571: 567: 563: 560: 556: 552: 551:least squares 544: 542: 540: 535: 533: 529: 525: 521: 518: |  517: 513: 509: 505: 501: 497: 493: 489: 485: 481: 477: 473: 470: 466: 463: 459: 456:is a form of 455: 451: 439: 434: 432: 427: 425: 420: 419: 417: 416: 411: 406: 401: 400: 399: 398: 393: 390: 388: 385: 383: 380: 378: 375: 373: 370: 368: 365: 364: 363: 362: 357: 352: 349: 347: 344: 342: 339: 337: 334: 332: 329: 328: 327: 326: 321: 318: 316: 313: 311: 308: 306: 303: 301: 298: 297: 296: 295: 290: 287: 285: 282: 280: 277: 275: 272: 271: 270: 269: 264: 261: 259: 256: 254: 253:Least squares 251: 250: 249: 248: 243: 238: 235: 234: 233: 232: 227: 224: 222: 219: 217: 214: 212: 209: 207: 204: 202: 199: 197: 194: 192: 189: 187: 186:Nonparametric 184: 182: 179: 178: 177: 176: 171: 168: 166: 163: 161: 158: 156: 155:Fixed effects 153: 151: 148: 147: 146: 145: 140: 137: 135: 132: 130: 129:Ordered logit 127: 125: 122: 120: 117: 115: 112: 110: 107: 105: 102: 100: 97: 95: 92: 90: 87: 85: 82: 80: 77: 76: 75: 74: 69: 66: 64: 61: 59: 56: 54: 51: 50: 49: 48: 43: 40: 36: 32: 31: 19: 7259:Applications 7098: 6976:Non-standard 6951: 6731: 6719: 6700: 6693: 6605:Econometrics 6555: / 6538:Chemometrics 6515:Epidemiology 6508: / 6481:Applications 6323:ARIMA model 6270:Q-statistic 6219:Stationarity 6115:Multivariate 6058: / 6054: / 6052:Multivariate 6050: / 5990: / 5986: / 5760:Bayes factor 5659:Signed rank 5571: 5545: 5537: 5525: 5220:Completeness 5056:Cohort study 4954:Opinion poll 4889:Missing data 4876:Study design 4831:Scatter plot 4753:Scatter plot 4746:Spearman's ρ 4708:Grouped data 4406:. Retrieved 4402: 4392: 4381:. Retrieved 4366: 4359: 4340: 4334: 4310:(1): 20–22. 4307: 4303: 4290: 4270: 4263: 4254: 4245: 4233:. Retrieved 4229: 4219: 4194: 4190: 4180: 4163: 4159: 4150: 4129: 4125: 4116: 4110:: 1471–1490. 4107: 4101: 4091: 4080:. Retrieved 4078:. 2018-10-03 4075: 4066: 3990: 3975: 3962: 3938: 3934: 3927: 3923: 3919: 3723: 3701: 3697: 3694: 3391: 3342: 2325: 2321: 2258: 2254: 2252: 2134: 2060: 1526: 1522: 1518: 1463: 1352: 1170: 1160: 1156: 1141: 1134: 1128: 986: 982: 980: 975: 971: 967: 914: 906: 902: 894: 890: 886: 882: 817: 813: 811: 722: 714: 710: 706: 702: 696: 629: 625: 623: 576:. The first 548: 536: 519: 515: 507: 506:). Although 503: 499: 498:, denoted E( 495: 487: 483: 475: 471: 464: 453: 447: 310:Non-negative 62: 6733:WikiProject 6648:Cartography 6610:Jurimetrics 6562:Reliability 6293:Time domain 6272:(Ljung–Box) 6194:Time-series 6072:Categorical 6056:Time-series 6048:Categorical 5983:(Bernoulli) 5818:Correlation 5798:Correlation 5594:Jarque–Bera 5566:Chi-squared 5328:M-estimator 5281:Asymptotics 5225:Sufficiency 4992:Interaction 4904:Replication 4884:Effect size 4841:Violin plot 4821:Radar chart 4801:Forest plot 4791:Correlogram 4741:Kendall's τ 1466:-th row of 901:changes in 320:Regularized 284:Generalized 216:Least angle 114:Mixed logit 7134:Background 7097:Mallows's 6600:Demography 6318:ARMA model 6123:Regression 5700:(Friedman) 5661:(Wilcoxon) 5599:Normality 5589:Lilliefors 5536:Student's 5412:Resampling 5286:Robustness 5274:divergence 5264:Efficiency 5202:(monotone) 5197:Likelihood 5114:Population 4947:Stratified 4899:Population 4718:Dependence 4674:Count data 4605:Percentile 4582:Dispersion 4515:Arithmetic 4450:Statistics 4408:22 January 4383:2020-08-28 4191:Biometrika 4082:2024-08-25 4059:References 3978:kernelized 3948:, such as 2140:estimation 1131:estimation 582:experiment 562:estimators 541:settings. 524:parameters 480:polynomial 478:th degree 450:statistics 359:Background 263:Non-linear 245:Estimation 7209:Numerical 5981:Logistic 5748:posterior 5674:Rank sum 5422:Jackknife 5417:Bootstrap 5235:Bootstrap 5170:Parameter 5119:Statistic 4914:Statistic 4826:Run chart 4811:Pie chart 4806:Histogram 4796:Fan chart 4771:Bar chart 4653:L-moments 4540:Geometric 3993:residuals 3970:smoothing 3937:far from 3890:… 3854:φ 3849:→ 3805:φ 3790:∈ 3778:φ 3739:∈ 3661:^ 3638:− 3608:− 3598:β 3496:β 3489:⋯ 3467:β 3444:β 3421:β 3411:^ 3371:β 3356:β 3279:∑ 3271:⋯ 3222:∑ 3172:∑ 3122:∑ 3093:β 3085:⋯ 3072:β 3058:β 3044:β 2989:∑ 2983:… 2940:∑ 2896:∑ 2858:∑ 2850:⋮ 2845:⋱ 2840:⋮ 2835:⋮ 2830:⋮ 2785:∑ 2779:⋯ 2742:∑ 2704:∑ 2666:∑ 2620:∑ 2614:⋯ 2577:∑ 2539:∑ 2501:∑ 2461:∑ 2455:⋯ 2418:∑ 2380:∑ 2342:∑ 2253:assuming 2231:→ 2202:− 2166:^ 2161:→ 2158:β 2113:→ 2110:ε 2098:→ 2095:β 2078:→ 2029:ε 2021:⋮ 2008:ε 1994:ε 1980:ε 1951:β 1943:⋮ 1930:β 1916:β 1902:β 1865:… 1824:⋮ 1819:⋱ 1814:⋮ 1809:⋮ 1804:⋮ 1780:… 1722:… 1664:… 1594:⋮ 1502:→ 1447:→ 1444:ε 1418:→ 1415:β 1389:→ 1329:… 1296:ε 1268:β 1261:⋯ 1234:β 1211:β 1198:β 1110:ε 1088:β 1081:⋯ 1059:β 1036:β 1020:β 1007:β 942:β 926:β 897:+1.) For 842:β 829:β 793:ε 771:β 755:β 742:β 701:variable 678:ε 663:β 650:β 620:approach. 598:inference 226:Segmented 7358:Category 7039:Logistic 7029:Binomial 7008:Isotonic 7003:Quantile 6695:Category 6388:Survival 6265:Johansen 5988:Binomial 5943:Isotonic 5530:(normal) 5175:location 4982:Blocking 4937:Sampling 4816:Q–Q plot 4781:Box plot 4763:Graphics 4658:Skewness 4648:Kurtosis 4620:Variance 4550:Heronian 4545:Harmonic 4007:See also 3958:wavelets 586:Gergonne 570:Legendre 559:unbiased 555:variance 467:and the 341:Bayesian 279:Weighted 274:Ordinary 206:Isotonic 201:Quantile 7034:Poisson 6721:Commons 6668:Kriging 6553:Process 6510:studies 6369:Wavelet 6202:General 5369:Plug-in 5163:L space 4942:Cluster 4643:Moments 4461:Outline 4324:2685560 4211:2331929 3984:with a 3950:splines 3821:, e.g. 1159:,  720:units. 618:ScheffĂŠ 557:of the 545:History 502: | 300:Partial 139:Poisson 6998:Robust 6590:Census 6180:Normal 6128:Manova 5948:Robust 5698:2-way 5690:1-way 5528:-test 5199:  4776:Biplot 4567:Median 4560:Lehmer 4502:Center 4374:  4347:  4322:  4278:  4235:30 Jan 4209:  3956:, and 3528:Where: 1305:  985:as an 699:scalar 594:design 580:of an 578:design 258:Linear 196:Robust 119:Probit 45:Models 6214:Trend 5743:prior 5685:anova 5574:-test 5548:-test 5540:-test 5447:Power 5392:Pivot 5185:shape 5180:scale 4630:Shape 4610:Range 4555:Heinz 4530:Cubic 4466:Index 4320:JSTOR 4207:JSTOR 4049:Notes 3995:have 2283:is a 2257:< 2142:) is 574:Gauss 305:Total 221:Local 7348:PhET 6778:and 6447:Test 5647:Sign 5499:Wald 4572:Mode 4510:Mean 4410:2017 4372:ISBN 4345:ISBN 4276:ISBN 4237:2024 3999:, a 3700:and 3347:for 1521:and 1488:and 974:and 596:and 528:data 7113:BIC 7108:AIC 5627:BIC 5622:AIC 4312:doi 4199:doi 4168:doi 4138:doi 3991:If 816:to 494:of 482:in 448:In 7360:: 7346:, 4401:. 4318:. 4308:52 4306:. 4253:. 4228:. 4205:. 4195:12 4193:. 4189:. 4162:. 4128:. 4108:11 4106:. 4100:. 4074:. 3988:. 3952:, 1533:: 1140:, 917:: 534:. 452:, 7101:p 7099:C 6845:) 6836:( 6768:e 6761:t 6754:v 5572:G 5546:F 5538:t 5526:Z 5245:V 5240:U 4442:e 4435:t 4428:v 4412:. 4386:. 4353:. 4326:. 4314:: 4284:. 4257:. 4239:. 4213:. 4201:: 4174:. 4170:: 4164:1 4144:. 4140:: 4130:1 4085:. 3942:0 3939:x 3935:x 3931:0 3928:x 3924:x 3920:y 3906:] 3901:d 3897:x 3893:, 3887:, 3882:2 3878:x 3874:, 3871:x 3868:, 3865:1 3862:[ 3841:] 3838:x 3835:, 3832:1 3829:[ 3801:d 3795:R 3787:) 3784:x 3781:( 3754:x 3750:d 3744:R 3736:x 3702:x 3698:x 3667:= 3658:y 3644:) 3641:m 3635:0 3632:( 3628:x 3619:= 3614:) 3611:m 3605:0 3602:( 3583:= 3580:m 3564:i 3560:y 3554:i 3550:x 3541:= 3538:n 3510:m 3506:x 3500:m 3492:+ 3486:+ 3481:2 3477:x 3471:2 3463:+ 3458:1 3454:x 3448:1 3440:+ 3435:0 3431:x 3425:0 3417:= 3408:y 3375:m 3360:0 3327:] 3319:m 3314:i 3310:x 3304:i 3300:y 3294:n 3289:1 3286:= 3283:i 3262:2 3257:i 3253:x 3247:i 3243:y 3237:n 3232:1 3229:= 3226:i 3212:1 3207:i 3203:x 3197:i 3193:y 3187:n 3182:1 3179:= 3176:i 3162:0 3157:i 3153:x 3147:i 3143:y 3137:n 3132:1 3129:= 3126:i 3115:[ 3110:= 3105:] 3097:m 3076:2 3062:1 3048:0 3037:[ 3030:] 3022:m 3019:2 3014:i 3010:x 3004:n 2999:1 2996:= 2993:i 2976:2 2973:+ 2970:m 2965:i 2961:x 2955:n 2950:1 2947:= 2944:i 2932:1 2929:+ 2926:m 2921:i 2917:x 2911:n 2906:1 2903:= 2900:i 2888:m 2883:i 2879:x 2873:n 2868:1 2865:= 2862:i 2821:2 2818:+ 2815:m 2810:i 2806:x 2800:n 2795:1 2792:= 2789:i 2772:4 2767:i 2763:x 2757:n 2752:1 2749:= 2746:i 2734:3 2729:i 2725:x 2719:n 2714:1 2711:= 2708:i 2696:2 2691:i 2687:x 2681:n 2676:1 2673:= 2670:i 2656:1 2653:+ 2650:m 2645:i 2641:x 2635:n 2630:1 2627:= 2624:i 2607:3 2602:i 2598:x 2592:n 2587:1 2584:= 2581:i 2569:2 2564:i 2560:x 2554:n 2549:1 2546:= 2543:i 2531:1 2526:i 2522:x 2516:n 2511:1 2508:= 2505:i 2491:m 2486:i 2482:x 2476:n 2471:1 2468:= 2465:i 2448:2 2443:i 2439:x 2433:n 2428:1 2425:= 2422:i 2410:1 2405:i 2401:x 2395:n 2390:1 2387:= 2384:i 2372:0 2367:i 2363:x 2357:n 2352:1 2349:= 2346:i 2335:[ 2300:i 2296:x 2270:X 2259:n 2255:m 2237:, 2228:y 2219:T 2213:X 2205:1 2198:) 2193:X 2186:T 2180:X 2175:( 2172:= 2119:. 2104:+ 2088:X 2084:= 2075:y 2046:, 2041:] 2033:n 2012:3 1998:2 1984:1 1973:[ 1968:+ 1963:] 1955:m 1934:2 1920:1 1906:0 1895:[ 1888:] 1880:m 1875:n 1871:x 1858:2 1853:n 1849:x 1841:n 1837:x 1831:1 1795:m 1790:3 1786:x 1773:2 1768:3 1764:x 1756:3 1752:x 1746:1 1737:m 1732:2 1728:x 1715:2 1710:2 1706:x 1698:2 1694:x 1688:1 1679:m 1674:1 1670:x 1657:2 1652:1 1648:x 1640:1 1636:x 1630:1 1624:[ 1619:= 1614:] 1606:n 1602:y 1585:3 1581:y 1571:2 1567:y 1557:1 1553:y 1546:[ 1527:i 1523:y 1519:x 1499:y 1475:X 1464:i 1386:y 1362:X 1338:) 1335:n 1332:, 1326:, 1323:2 1320:, 1317:1 1314:= 1311:i 1308:( 1300:i 1292:+ 1287:m 1282:i 1278:x 1272:m 1264:+ 1258:+ 1253:2 1248:i 1244:x 1238:2 1230:+ 1225:i 1221:x 1215:1 1207:+ 1202:0 1193:= 1187:i 1183:y 1161:x 1157:x 1145:1 1142:β 1138:0 1135:β 1113:. 1107:+ 1102:n 1098:x 1092:n 1084:+ 1078:+ 1073:3 1069:x 1063:3 1055:+ 1050:2 1046:x 1040:2 1032:+ 1029:x 1024:1 1016:+ 1011:0 1003:= 1000:y 987:n 983:y 976:y 972:x 968:x 954:. 951:x 946:2 938:2 935:+ 930:1 915:x 907:y 903:x 895:x 891:x 887:x 883:x 869:. 866:) 863:1 860:+ 857:x 854:2 851:( 846:2 838:+ 833:1 818:x 814:x 796:. 790:+ 785:2 781:x 775:2 767:+ 764:x 759:1 751:+ 746:0 738:= 735:y 718:1 715:β 711:y 707:x 703:x 681:, 675:+ 672:x 667:1 659:+ 654:0 646:= 643:y 630:x 626:y 520:x 516:y 504:x 500:y 496:y 488:x 484:x 476:n 472:y 465:x 437:e 430:t 423:v 20:)

Index

Polynomial least squares
Regression analysis
Linear regression
Simple regression
Polynomial regression
General linear model
Generalized linear model
Vector generalized linear model
Discrete choice
Binomial regression
Binary regression
Logistic regression
Multinomial logistic regression
Mixed logit
Probit
Multinomial probit
Ordered logit
Ordered probit
Poisson
Multilevel model
Fixed effects
Random effects
Linear mixed-effects model
Nonlinear mixed-effects model
Nonlinear regression
Nonparametric
Semiparametric
Robust
Quantile
Isotonic

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