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Linear model

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as a linear function of past values of the same time series and of current and past values of the innovations. This particular aspect of the structure means that it is relatively simple to derive relations for the mean and
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There are some other instances where "nonlinear model" is used to contrast with a linearly structured model, although the term "linear model" is not usually applied. One example of this is
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with a different meaning. In each case, the designation "linear" is used to identify a subclass of models for which substantial reduction in the complexity of the related
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in a linear way in the above relationship. Alternatively, one may say that the predicted values corresponding to the above model, namely
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at later times. In this instance the use of the term "linear model" refers to the structure of the above relationship in representing
396:{\displaystyle Y_{i}=\beta _{0}+\beta _{1}\phi _{1}(X_{i1})+\cdots +\beta _{p}\phi _{p}(X_{ip})+\varepsilon _{i}\qquad i=1,\ldots ,n} 3307: 3199: 1590: 82: 3912: 3485: 3359: 49:
in the system. The most common occurrence is in connection with regression models and the term is often taken as synonymous with
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properties of the time series. Note that here the "linear" part of the term "linear model" is not referring to the coefficients
684:{\displaystyle {\hat {Y}}_{i}=\beta _{0}+\beta _{1}\phi _{1}(X_{i1})+\cdots +\beta _{p}\phi _{p}(X_{ip})\qquad (i=1,\ldots ,n),} 3543: 3204: 2949: 2320: 1910: 2534: 3594: 2806: 2613: 2502: 2460: 1407: 1699: 3837: 2796: 2846: 3388: 3337: 3322: 3312: 3181: 3053: 3020: 2801: 2631: 1369:{\displaystyle X_{t}=c+\varepsilon _{t}+\sum _{i=1}^{p}\phi _{i}X_{t-i}+\sum _{i=1}^{q}\theta _{i}\varepsilon _{t-i}.\,} 3457: 2758: 3732: 3533: 2512: 2181: 1645: 3617: 3584: 3939: 3589: 3332: 3091: 2997: 2977: 2885: 2596: 2414: 1897: 1769: 31: 2763: 2529: 2387: 3349: 3117: 2838: 2692: 2621: 2541: 2399: 2380: 2088: 1809: 1547: 409: 3462: 3832: 3599: 3147: 3112: 3076: 2861: 2303: 2212: 2171: 2083: 1774: 1613: 1542: 487:
representing errors in the relationship. The "linear" part of the designation relates to the appearance of the
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which makes it relatively easy to determine the statistical properties of the estimated values of
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From this, it can readily be seen that the "linear" aspect of the model means the following:
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which are new random effects that appear at a certain time but also affect values of
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the derivatives of the function are linear functions of the
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the function to be minimised is a quadratic function of the
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are determined by minimising a sum of squares function
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for which minimisation is a relatively simple problem;
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Given that estimation is undertaken on the basis of a
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Autoregressive conditional heteroskedasticity (ARCH)
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However, the term is also used in 1500: 1494: 1473: 1467: 1441: 1435: 1415: 1390: 1384: 1365: 1350: 1340: 1330: 1319: 1300: 1290: 1280: 1269: 1256: 1237: 1231: 1207: 1201: 1165: 1159: 1138: 1132: 1111: 1105: 1081: 1075: 1070:are linear functions of the observations 1054: 1048: 1024: 1018: 994: 988: 955: 938: 925: 915: 890: 877: 867: 854: 841: 825: 814: 801: 796: 786: 775: 763: 739: 733: 705: 699: 638: 625: 615: 590: 577: 567: 554: 541: 530: 529: 526: 502: 496: 467: 461: 436: 417: 411: 365: 346: 333: 323: 298: 285: 275: 262: 249: 243: 216: 210: 186: 180: 143: 128: 106: 93: 84: 456:functions. In the above, the quantities 1574: 79:is as follows. Given a (random) sample 3585:Kaplan–Meier estimator (product limit) 175:the relation between the observations 7: 3895: 3595:Accelerated failure time (AFT) model 3907: 3190:Analysis of variance (ANOVA, anova) 1194:autoregressive moving average model 3285:Cochran–Mantel–Haenszel statistics 1911:Pearson product-moment correlation 1526:nonlinear dimensionality reduction 1406:are random variables representing 45:refers to any model which assumes 25: 3906: 3894: 3882: 3869: 3868: 1399:{\displaystyle \varepsilon _{i}} 1147:{\displaystyle \varepsilon _{i}} 476:{\displaystyle \varepsilon _{i}} 3544:Least-squares spectral analysis 650: 371: 2525:Mean-unbiased minimum-variance 947: 931: 899: 883: 675: 651: 647: 631: 599: 583: 535: 355: 339: 307: 291: 137: 86: 1: 3838:Geographic information system 3054:Simultaneous equations models 1196:. Here the model for values { 75:For the regression case, the 3021:Coefficient of determination 2632:Uniformly most powerful test 694:are linear functions of the 3590:Proportional hazards models 3534:Spectral density estimation 3516:Vector autoregression (VAR) 2950:Maximum posterior estimator 2182:Randomized controlled trial 1509:{\displaystyle \theta _{i}} 1379:where again the quantities 3956: 3350:Multivariate distributions 1770:Average absolute deviation 1174:{\displaystyle \beta _{j}} 1120:{\displaystyle \beta _{j}} 1063:{\displaystyle \beta _{j}} 1033:{\displaystyle \beta _{j}} 1003:{\displaystyle \beta _{j}} 748:{\displaystyle \beta _{j}} 714:{\displaystyle \beta _{j}} 511:{\displaystyle \beta _{j}} 68: 32:linear model of innovation 29: 3864: 3667: 3654: 3338:Structural equation model 3246: 3221: 2992: 2968: 2700: 2674:Score/Lagrange multiplier 2280: 2267: 2089:Sample size determination 2050: 2037: 1667: 1654: 1636: 1548:Linear predictor function 1482:{\displaystyle \phi _{i}} 27:Type of statistical model 3833:Environmental statistics 3355:Elliptical distributions 3148:Generalized linear model 3077:Simple linear regression 2847:Hodges–Lehmann estimator 2304:Probability distribution 2213:Stochastic approximation 1775:Coefficient of variation 1543:Generalized linear model 1520:Other uses in statistics 65:Linear regression models 30:Not to be confused with 3493:Cross-correlation (XCF) 3101:Non-standard predictors 2535:Lehmann–ScheffĂ© theorem 2208:Adaptive clinical trial 1581:Priestley, M.B. (1988) 1100:the minimising values 1043:the minimising values 489:regression coefficients 3889:Mathematics portal 3710:Engineering statistics 3618:Nelson–Aalen estimator 3195:Analysis of covariance 3082:Ordinary least squares 3006:Pearson product-moment 2410:Statistical functional 2321:Empirical distribution 2154:Controlled experiments 1883:Frequency distribution 1661:Descriptive statistics 1510: 1483: 1451: 1424: 1400: 1370: 1335: 1285: 1217: 1175: 1148: 1121: 1091: 1064: 1034: 1004: 968: 830: 791: 749: 715: 685: 512: 477: 446: 397: 229: 228:{\displaystyle X_{ij}} 196: 169: 3805:Population statistics 3747:System identification 3481:Autocorrelation (ACF) 3409:Exponential smoothing 3323:Discriminant analysis 3318:Canonical correlation 3182:Partition of variance 3044:Regression validation 2888:(Jonckheere–Terpstra) 2787:Likelihood-ratio test 2476:Frequentist inference 2388:Location–scale family 2309:Sampling distribution 2274:Statistical inference 2241:Cross-sectional study 2228:Observational studies 2187:Randomized experiment 2016:Stem-and-leaf display 1818:Central limit theorem 1511: 1484: 1452: 1450:{\displaystyle X_{t}} 1425: 1401: 1371: 1315: 1265: 1218: 1216:{\displaystyle X_{t}} 1176: 1149: 1122: 1092: 1090:{\displaystyle Y_{i}} 1065: 1035: 1005: 969: 810: 771: 750: 716: 686: 513: 478: 447: 398: 230: 204:independent variables 197: 195:{\displaystyle Y_{i}} 170: 3728:Probabilistic design 3313:Principal components 3156:Exponential families 3108:Nonlinear regression 3087:General linear model 3049:Mixed effects models 3039:Errors and residuals 3016:Confounding variable 2918:Bayesian probability 2896:Van der Waerden test 2886:Ordered alternative 2651:Multiple comparisons 2530:Rao–Blackwellization 2493:Estimating equations 2449:Statistical distance 2167:Factorial experiment 1700:Arithmetic-Geometric 1538:General linear model 1493: 1466: 1434: 1414: 1383: 1230: 1200: 1158: 1131: 1104: 1074: 1047: 1017: 987: 762: 732: 698: 525: 495: 460: 410: 242: 209: 179: 83: 55:time series analysis 3800:Official statistics 3723:Methods engineering 3404:Seasonal adjustment 3172:Poisson regressions 3092:Bayesian regression 3031:Regression analysis 3011:Partial correlation 2983:Regression analysis 2582:Prediction interval 2577:Likelihood interval 2567:Confidence interval 2559:Interval estimation 2520:Unbiased estimators 2338:Model specification 2218:Up-and-down designs 1906:Partial correlation 1862:Index of dispersion 1780:Interquartile range 806: 3820:Spatial statistics 3700:Medical statistics 3600:First hitting time 3554:Whittle likelihood 3205:Degrees of freedom 3200:Multivariate ANOVA 3133:Heteroscedasticity 2945:Bayesian estimator 2910:Bayesian inference 2759:Kolmogorov–Smirnov 2644:Randomization test 2614:Testing hypotheses 2587:Tolerance interval 2498:Maximum likelihood 2393:Exponential family 2326:Density estimation 2286:Statistical theory 2246:Natural experiment 2192:Scientific control 2109:Survey methodology 1795:Standard deviation 1585:, Academic Press. 1506: 1479: 1447: 1420: 1396: 1366: 1213: 1188:Time series models 1171: 1144: 1117: 1087: 1060: 1030: 1000: 964: 792: 745: 711: 681: 508: 473: 442: 393: 225: 192: 165: 59:statistical theory 3940:Regression models 3922: 3921: 3860: 3859: 3856: 3855: 3795:National accounts 3765:Actuarial science 3757:Social statistics 3650: 3649: 3646: 3645: 3642: 3641: 3577:Survival function 3562: 3561: 3424:Granger causality 3265:Contingency table 3240:Survival analysis 3217: 3216: 3213: 3212: 3069:Linear regression 2964: 2963: 2960: 2959: 2935:Credible interval 2904: 2903: 2687: 2686: 2503:Method of moments 2372:Parametric family 2333:Statistical model 2263: 2262: 2259: 2258: 2177:Random assignment 2099:Statistical power 2033: 2032: 2029: 2028: 1878:Contingency table 1848: 1847: 1715:Generalized/power 1563:Statistical model 1558:Linear regression 1423:{\displaystyle X} 538: 235:is formulated as 77:statistical model 71:Linear regression 51:linear regression 16:(Redirected from 3947: 3910: 3909: 3898: 3897: 3887: 3886: 3872: 3871: 3775:Crime statistics 3669: 3656: 3573: 3539:Fourier analysis 3526:Frequency domain 3506: 3453: 3419:Structural break 3379: 3328:Cluster analysis 3275:Log-linear model 3248: 3223: 3164: 3138:Homoscedasticity 2994: 2970: 2889: 2881: 2873: 2872:(Kruskal–Wallis) 2857: 2842: 2797:Cross validation 2782: 2764:Anderson–Darling 2711: 2698: 2669:Likelihood-ratio 2661:Parametric tests 2639:Permutation test 2622:1- & 2-tails 2513:Minimum distance 2485:Point estimation 2481: 2432:Optimal decision 2383: 2282: 2269: 2251:Quasi-experiment 2201:Adaptive designs 2052: 2039: 1916:Rank correlation 1678: 1669: 1656: 1623: 1616: 1609: 1600: 1593: 1579: 1515: 1513: 1512: 1507: 1505: 1504: 1488: 1486: 1485: 1480: 1478: 1477: 1456: 1454: 1453: 1448: 1446: 1445: 1429: 1427: 1426: 1421: 1405: 1403: 1402: 1397: 1395: 1394: 1375: 1373: 1372: 1367: 1361: 1360: 1345: 1344: 1334: 1329: 1311: 1310: 1295: 1294: 1284: 1279: 1261: 1260: 1242: 1241: 1222: 1220: 1219: 1214: 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3918: 3881: 3852: 3814: 3751: 3737:quality control 3704: 3686:Clinical trials 3663: 3638: 3622: 3610:Hazard function 3604: 3558: 3520: 3504: 3467: 3463:Breusch–Godfrey 3451: 3428: 3368: 3343:Factor analysis 3289: 3270:Graphical model 3242: 3209: 3176: 3162: 3142: 3096: 3063: 3025: 2988: 2987: 2956: 2900: 2887: 2879: 2871: 2855: 2840: 2819:Rank statistics 2813: 2792:Model selection 2780: 2738:Goodness of fit 2732: 2709: 2683: 2655: 2608: 2553: 2542:Median unbiased 2470: 2381: 2314:Order statistic 2276: 2255: 2222: 2196: 2148: 2103: 2046: 2044:Data collection 2025: 1937: 1892: 1866: 1844: 1804: 1756: 1673:Continuous data 1663: 1650: 1632: 1627: 1597: 1596: 1580: 1576: 1571: 1534: 1522: 1496: 1491: 1490: 1469: 1464: 1463: 1437: 1432: 1431: 1412: 1411: 1386: 1381: 1380: 1346: 1336: 1296: 1286: 1252: 1233: 1228: 1227: 1203: 1198: 1197: 1190: 1161: 1156: 1155: 1134: 1129: 1128: 1107: 1102: 1101: 1077: 1072: 1071: 1050: 1045: 1044: 1020: 1015: 1014: 990: 985: 984: 934: 921: 911: 886: 873: 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3518: 3513: 3508: 3500: 3495: 3490: 3489: 3488: 3486:partial (PACF) 3477: 3475: 3469: 3468: 3466: 3465: 3460: 3455: 3447: 3442: 3436: 3434: 3433:Specific tests 3430: 3429: 3427: 3426: 3421: 3416: 3411: 3406: 3401: 3396: 3391: 3385: 3383: 3376: 3370: 3369: 3367: 3366: 3365: 3364: 3363: 3362: 3347: 3346: 3345: 3335: 3333:Classification 3330: 3325: 3320: 3315: 3310: 3305: 3299: 3297: 3291: 3290: 3288: 3287: 3282: 3280:McNemar's test 3277: 3272: 3267: 3262: 3256: 3254: 3244: 3243: 3226: 3219: 3218: 3215: 3214: 3211: 3210: 3208: 3207: 3202: 3197: 3192: 3186: 3184: 3178: 3177: 3175: 3174: 3158: 3152: 3150: 3144: 3143: 3141: 3140: 3135: 3130: 3125: 3120: 3118:Semiparametric 3115: 3110: 3104: 3102: 3098: 3097: 3095: 3094: 3089: 3084: 3079: 3073: 3071: 3065: 3064: 3062: 3061: 3056: 3051: 3046: 3041: 3035: 3033: 3027: 3026: 3024: 3023: 3018: 3013: 3008: 3002: 3000: 2990: 2989: 2986: 2985: 2980: 2974: 2973: 2966: 2965: 2962: 2961: 2958: 2957: 2955: 2954: 2953: 2952: 2942: 2937: 2932: 2931: 2930: 2925: 2914: 2912: 2906: 2905: 2902: 2901: 2899: 2898: 2893: 2892: 2891: 2883: 2875: 2859: 2856:(Mann–Whitney) 2851: 2850: 2849: 2836: 2835: 2834: 2823: 2821: 2815: 2814: 2812: 2811: 2810: 2809: 2804: 2799: 2789: 2784: 2781:(Shapiro–Wilk) 2776: 2771: 2766: 2761: 2756: 2748: 2742: 2740: 2734: 2733: 2731: 2730: 2722: 2713: 2701: 2695: 2693:Specific tests 2689: 2688: 2685: 2684: 2682: 2681: 2676: 2671: 2665: 2663: 2657: 2656: 2654: 2653: 2648: 2647: 2646: 2636: 2635: 2634: 2624: 2618: 2616: 2610: 2609: 2607: 2606: 2605: 2604: 2599: 2589: 2584: 2579: 2574: 2569: 2563: 2561: 2555: 2554: 2552: 2551: 2546: 2545: 2544: 2539: 2538: 2537: 2532: 2517: 2516: 2515: 2510: 2505: 2500: 2489: 2487: 2478: 2472: 2471: 2469: 2468: 2463: 2458: 2457: 2456: 2446: 2441: 2440: 2439: 2429: 2428: 2427: 2422: 2417: 2407: 2402: 2397: 2396: 2395: 2390: 2385: 2369: 2368: 2367: 2362: 2357: 2347: 2346: 2345: 2340: 2330: 2329: 2328: 2318: 2317: 2316: 2306: 2301: 2296: 2290: 2288: 2278: 2277: 2272: 2265: 2264: 2261: 2260: 2257: 2256: 2254: 2253: 2248: 2243: 2238: 2232: 2230: 2224: 2223: 2221: 2220: 2215: 2210: 2204: 2202: 2198: 2197: 2195: 2194: 2189: 2184: 2179: 2174: 2169: 2164: 2158: 2156: 2150: 2149: 2147: 2146: 2144:Standard error 2141: 2136: 2131: 2130: 2129: 2124: 2113: 2111: 2105: 2104: 2102: 2101: 2096: 2091: 2086: 2081: 2076: 2074:Optimal design 2071: 2066: 2060: 2058: 2048: 2047: 2042: 2035: 2034: 2031: 2030: 2027: 2026: 2024: 2023: 2018: 2013: 2008: 2003: 1998: 1993: 1988: 1983: 1978: 1973: 1968: 1963: 1958: 1953: 1947: 1945: 1939: 1938: 1936: 1935: 1930: 1929: 1928: 1923: 1913: 1908: 1902: 1900: 1894: 1893: 1891: 1890: 1885: 1880: 1874: 1872: 1871:Summary tables 1868: 1867: 1865: 1864: 1858: 1856: 1850: 1849: 1846: 1845: 1843: 1842: 1841: 1840: 1835: 1830: 1820: 1814: 1812: 1806: 1805: 1803: 1802: 1797: 1792: 1787: 1782: 1777: 1772: 1766: 1764: 1758: 1757: 1755: 1754: 1749: 1744: 1743: 1742: 1737: 1732: 1727: 1722: 1717: 1712: 1707: 1705:Contraharmonic 1702: 1697: 1686: 1684: 1675: 1665: 1664: 1659: 1652: 1651: 1649: 1648: 1643: 1637: 1634: 1633: 1628: 1626: 1625: 1618: 1611: 1603: 1595: 1594: 1573: 1572: 1570: 1567: 1566: 1565: 1560: 1555: 1550: 1545: 1540: 1533: 1530: 1521: 1518: 1503: 1499: 1476: 1472: 1444: 1440: 1419: 1393: 1389: 1377: 1376: 1364: 1359: 1356: 1353: 1349: 1343: 1339: 1333: 1328: 1325: 1322: 1318: 1314: 1309: 1306: 1303: 1299: 1293: 1289: 1283: 1278: 1275: 1272: 1268: 1264: 1259: 1255: 1251: 1248: 1245: 1240: 1236: 1210: 1206: 1189: 1186: 1185: 1184: 1183: 1182: 1168: 1164: 1141: 1137: 1114: 1110: 1098: 1084: 1080: 1057: 1053: 1041: 1027: 1023: 1011: 997: 993: 975: 974: 963: 958: 953: 949: 944: 941: 937: 933: 928: 924: 918: 914: 910: 907: 904: 901: 896: 893: 889: 885: 880: 876: 870: 866: 862: 857: 853: 849: 844: 840: 835: 828: 823: 820: 817: 813: 809: 804: 799: 795: 789: 784: 781: 778: 774: 770: 767: 742: 738: 708: 704: 692: 691: 680: 677: 674: 671: 668: 665: 662: 659: 656: 653: 649: 644: 641: 637: 633: 628: 624: 618: 614: 610: 607: 604: 601: 596: 593: 589: 585: 580: 576: 570: 566: 562: 557: 553: 549: 544: 537: 534: 505: 501: 470: 466: 439: 435: 431: 428: 425: 420: 416: 404: 403: 392: 389: 386: 383: 380: 377: 374: 368: 364: 360: 357: 352: 349: 345: 341: 336: 332: 326: 322: 318: 315: 312: 309: 304: 301: 297: 293: 288: 284: 278: 274: 270: 265: 261: 257: 252: 248: 222: 219: 215: 189: 185: 164: 161: 158: 155: 152: 149: 146: 142: 139: 134: 131: 127: 123: 120: 117: 112: 109: 105: 101: 96: 92: 88: 69:Main article: 66: 63: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 3952: 3941: 3938: 3936: 3935:Curve fitting 3933: 3932: 3930: 3915: 3914: 3905: 3903: 3902: 3893: 3891: 3890: 3885: 3879: 3877: 3876: 3867: 3866: 3863: 3849: 3846: 3844: 3843:Geostatistics 3841: 3839: 3836: 3834: 3831: 3829: 3826: 3825: 3823: 3821: 3817: 3811: 3810:Psychometrics 3808: 3806: 3803: 3801: 3798: 3796: 3793: 3791: 3788: 3786: 3783: 3781: 3778: 3776: 3773: 3771: 3768: 3766: 3763: 3762: 3760: 3758: 3754: 3748: 3745: 3743: 3740: 3738: 3734: 3731: 3729: 3726: 3724: 3721: 3719: 3716: 3715: 3713: 3711: 3707: 3701: 3698: 3696: 3693: 3691: 3687: 3684: 3682: 3679: 3678: 3676: 3674: 3673:Biostatistics 3670: 3666: 3662: 3657: 3653: 3635: 3634:Log-rank test 3632: 3631: 3629: 3625: 3619: 3616: 3615: 3613: 3611: 3607: 3601: 3598: 3596: 3593: 3591: 3588: 3586: 3583: 3582: 3580: 3578: 3574: 3571: 3569: 3565: 3555: 3552: 3550: 3547: 3545: 3542: 3540: 3537: 3535: 3532: 3531: 3529: 3527: 3523: 3517: 3514: 3512: 3509: 3507: 3505:(Box–Jenkins) 3501: 3499: 3496: 3494: 3491: 3487: 3484: 3483: 3482: 3479: 3478: 3476: 3474: 3470: 3464: 3461: 3459: 3458:Durbin–Watson 3456: 3454: 3448: 3446: 3443: 3441: 3440:Dickey–Fuller 3438: 3437: 3435: 3431: 3425: 3422: 3420: 3417: 3415: 3414:Cointegration 3412: 3410: 3407: 3405: 3402: 3400: 3397: 3395: 3392: 3390: 3389:Decomposition 3387: 3386: 3384: 3380: 3377: 3375: 3371: 3361: 3358: 3357: 3356: 3353: 3352: 3351: 3348: 3344: 3341: 3340: 3339: 3336: 3334: 3331: 3329: 3326: 3324: 3321: 3319: 3316: 3314: 3311: 3309: 3306: 3304: 3301: 3300: 3298: 3296: 3292: 3286: 3283: 3281: 3278: 3276: 3273: 3271: 3268: 3266: 3263: 3261: 3260:Cohen's kappa 3258: 3257: 3255: 3253: 3249: 3245: 3241: 3237: 3233: 3229: 3224: 3220: 3206: 3203: 3201: 3198: 3196: 3193: 3191: 3188: 3187: 3185: 3183: 3179: 3173: 3169: 3165: 3159: 3157: 3154: 3153: 3151: 3149: 3145: 3139: 3136: 3134: 3131: 3129: 3126: 3124: 3121: 3119: 3116: 3114: 3113:Nonparametric 3111: 3109: 3106: 3105: 3103: 3099: 3093: 3090: 3088: 3085: 3083: 3080: 3078: 3075: 3074: 3072: 3070: 3066: 3060: 3057: 3055: 3052: 3050: 3047: 3045: 3042: 3040: 3037: 3036: 3034: 3032: 3028: 3022: 3019: 3017: 3014: 3012: 3009: 3007: 3004: 3003: 3001: 2999: 2995: 2991: 2984: 2981: 2979: 2976: 2975: 2971: 2967: 2951: 2948: 2947: 2946: 2943: 2941: 2938: 2936: 2933: 2929: 2926: 2924: 2921: 2920: 2919: 2916: 2915: 2913: 2911: 2907: 2897: 2894: 2890: 2884: 2882: 2876: 2874: 2868: 2867: 2866: 2863: 2862:Nonparametric 2860: 2858: 2852: 2848: 2845: 2844: 2843: 2837: 2833: 2832:Sample median 2830: 2829: 2828: 2825: 2824: 2822: 2820: 2816: 2808: 2805: 2803: 2800: 2798: 2795: 2794: 2793: 2790: 2788: 2785: 2783: 2777: 2775: 2772: 2770: 2767: 2765: 2762: 2760: 2757: 2755: 2753: 2749: 2747: 2744: 2743: 2741: 2739: 2735: 2729: 2727: 2723: 2721: 2719: 2714: 2712: 2707: 2703: 2702: 2699: 2696: 2694: 2690: 2680: 2677: 2675: 2672: 2670: 2667: 2666: 2664: 2662: 2658: 2652: 2649: 2645: 2642: 2641: 2640: 2637: 2633: 2630: 2629: 2628: 2625: 2623: 2620: 2619: 2617: 2615: 2611: 2603: 2600: 2598: 2595: 2594: 2593: 2590: 2588: 2585: 2583: 2580: 2578: 2575: 2573: 2570: 2568: 2565: 2564: 2562: 2560: 2556: 2550: 2547: 2543: 2540: 2536: 2533: 2531: 2528: 2527: 2526: 2523: 2522: 2521: 2518: 2514: 2511: 2509: 2506: 2504: 2501: 2499: 2496: 2495: 2494: 2491: 2490: 2488: 2486: 2482: 2479: 2477: 2473: 2467: 2464: 2462: 2459: 2455: 2452: 2451: 2450: 2447: 2445: 2442: 2438: 2437:loss function 2435: 2434: 2433: 2430: 2426: 2423: 2421: 2418: 2416: 2413: 2412: 2411: 2408: 2406: 2403: 2401: 2398: 2394: 2391: 2389: 2386: 2384: 2378: 2375: 2374: 2373: 2370: 2366: 2363: 2361: 2358: 2356: 2353: 2352: 2351: 2348: 2344: 2341: 2339: 2336: 2335: 2334: 2331: 2327: 2324: 2323: 2322: 2319: 2315: 2312: 2311: 2310: 2307: 2305: 2302: 2300: 2297: 2295: 2292: 2291: 2289: 2287: 2283: 2279: 2275: 2270: 2266: 2252: 2249: 2247: 2244: 2242: 2239: 2237: 2234: 2233: 2231: 2229: 2225: 2219: 2216: 2214: 2211: 2209: 2206: 2205: 2203: 2199: 2193: 2190: 2188: 2185: 2183: 2180: 2178: 2175: 2173: 2170: 2168: 2165: 2163: 2160: 2159: 2157: 2155: 2151: 2145: 2142: 2140: 2139:Questionnaire 2137: 2135: 2132: 2128: 2125: 2123: 2120: 2119: 2118: 2115: 2114: 2112: 2110: 2106: 2100: 2097: 2095: 2092: 2090: 2087: 2085: 2082: 2080: 2077: 2075: 2072: 2070: 2067: 2065: 2062: 2061: 2059: 2057: 2053: 2049: 2045: 2040: 2036: 2022: 2019: 2017: 2014: 2012: 2009: 2007: 2004: 2002: 1999: 1997: 1994: 1992: 1989: 1987: 1984: 1982: 1979: 1977: 1974: 1972: 1969: 1967: 1966:Control chart 1964: 1962: 1959: 1957: 1954: 1952: 1949: 1948: 1946: 1944: 1940: 1934: 1931: 1927: 1924: 1922: 1919: 1918: 1917: 1914: 1912: 1909: 1907: 1904: 1903: 1901: 1899: 1895: 1889: 1886: 1884: 1881: 1879: 1876: 1875: 1873: 1869: 1863: 1860: 1859: 1857: 1855: 1851: 1839: 1836: 1834: 1831: 1829: 1826: 1825: 1824: 1821: 1819: 1816: 1815: 1813: 1811: 1807: 1801: 1798: 1796: 1793: 1791: 1788: 1786: 1783: 1781: 1778: 1776: 1773: 1771: 1768: 1767: 1765: 1763: 1759: 1753: 1750: 1748: 1745: 1741: 1738: 1736: 1733: 1731: 1728: 1726: 1723: 1721: 1718: 1716: 1713: 1711: 1708: 1706: 1703: 1701: 1698: 1696: 1693: 1692: 1691: 1688: 1687: 1685: 1683: 1679: 1676: 1674: 1670: 1666: 1662: 1657: 1653: 1647: 1644: 1642: 1639: 1638: 1635: 1631: 1624: 1619: 1617: 1612: 1610: 1605: 1604: 1601: 1592: 1591:0-12-564911-8 1588: 1584: 1578: 1575: 1568: 1564: 1561: 1559: 1556: 1554: 1553:Linear system 1551: 1549: 1546: 1544: 1541: 1539: 1536: 1535: 1531: 1529: 1527: 1519: 1517: 1501: 1497: 1474: 1470: 1461: 1442: 1438: 1417: 1409: 1391: 1387: 1362: 1357: 1354: 1351: 1347: 1341: 1337: 1331: 1326: 1323: 1320: 1316: 1312: 1307: 1304: 1301: 1297: 1291: 1287: 1281: 1276: 1273: 1270: 1266: 1262: 1257: 1253: 1249: 1246: 1243: 1238: 1234: 1226: 1225: 1224: 1208: 1204: 1195: 1187: 1166: 1162: 1139: 1135: 1112: 1108: 1099: 1082: 1078: 1055: 1051: 1042: 1025: 1021: 1012: 995: 991: 982: 981: 980: 979: 978: 961: 956: 951: 942: 939: 935: 926: 922: 916: 912: 908: 905: 902: 894: 891: 887: 878: 874: 868: 864: 860: 855: 851: 847: 842: 838: 833: 826: 821: 818: 815: 811: 807: 802: 797: 793: 787: 782: 779: 776: 772: 768: 765: 758: 757: 756: 740: 736: 727: 726:least squares 722: 706: 702: 678: 672: 669: 666: 663: 660: 657: 654: 642: 639: 635: 626: 622: 616: 612: 608: 605: 602: 594: 591: 587: 578: 574: 568: 564: 560: 555: 551: 547: 542: 532: 521: 520: 519: 503: 499: 490: 486: 468: 464: 455: 437: 433: 429: 426: 423: 418: 414: 390: 387: 384: 381: 378: 375: 372: 366: 362: 358: 350: 347: 343: 334: 330: 324: 320: 316: 313: 310: 302: 299: 295: 286: 282: 276: 272: 268: 263: 259: 255: 250: 246: 238: 237: 236: 220: 217: 213: 205: 187: 183: 162: 159: 156: 153: 150: 147: 144: 140: 132: 129: 125: 121: 118: 115: 110: 107: 103: 99: 94: 90: 78: 72: 64: 62: 61:is possible. 60: 56: 52: 48: 44: 40: 33: 19: 18:Linear models 3911: 3899: 3880: 3873: 3785:Econometrics 3735: / 3718:Chemometrics 3695:Epidemiology 3688: / 3661:Applications 3503:ARIMA model 3450:Q-statistic 3399:Stationarity 3295:Multivariate 3238: / 3234: / 3232:Multivariate 3230: / 3170: / 3166: / 2940:Bayes factor 2839:Signed rank 2751: 2725: 2717: 2705: 2400:Completeness 2236:Cohort study 2134:Opinion poll 2069:Missing data 2056:Study design 2011:Scatter plot 1933:Scatter plot 1926:Spearman's ρ 1888:Grouped data 1582: 1577: 1523: 1378: 1191: 976: 723: 693: 405: 74: 43:linear model 42: 36: 3913:WikiProject 3828:Cartography 3790:Jurimetrics 3742:Reliability 3473:Time domain 3452:(Ljung–Box) 3374:Time-series 3252:Categorical 3236:Time-series 3228:Categorical 3163:(Bernoulli) 2998:Correlation 2978:Correlation 2774:Jarque–Bera 2746:Chi-squared 2508:M-estimator 2461:Asymptotics 2405:Sufficiency 2172:Interaction 2084:Replication 2064:Effect size 2021:Violin plot 2001:Radar chart 1981:Forest plot 1971:Correlogram 1921:Kendall's τ 1408:innovations 41:, the term 3929:Categories 3780:Demography 3498:ARMA model 3303:Regression 2880:(Friedman) 2841:(Wilcoxon) 2779:Normality 2769:Lilliefors 2716:Student's 2592:Resampling 2466:Robustness 2454:divergence 2444:Efficiency 2382:(monotone) 2377:Likelihood 2294:Population 2127:Stratified 2079:Population 1898:Dependence 1854:Count data 1785:Percentile 1762:Dispersion 1695:Arithmetic 1630:Statistics 1569:References 1460:covariance 39:statistics 3161:Logistic 2928:posterior 2854:Rank sum 2602:Jackknife 2597:Bootstrap 2415:Bootstrap 2350:Parameter 2299:Statistic 2094:Statistic 2006:Run chart 1991:Pie chart 1986:Histogram 1976:Fan chart 1951:Bar chart 1833:L-moments 1720:Geometric 1498:θ 1471:ϕ 1388:ε 1355:− 1348:ε 1338:θ 1317:∑ 1305:− 1288:ϕ 1267:∑ 1254:ε 1163:β 1136:ε 1109:β 1052:β 1022:β 992:β 923:ϕ 913:β 909:− 906:⋯ 903:− 875:ϕ 865:β 861:− 852:β 848:− 812:∑ 794:ε 773:∑ 737:β 703:β 667:… 623:ϕ 613:β 606:⋯ 575:ϕ 565:β 552:β 536:^ 500:β 465:ε 454:nonlinear 434:ϕ 427:… 415:ϕ 385:… 363:ε 331:ϕ 321:β 314:⋯ 283:ϕ 273:β 260:β 157:… 119:… 47:linearity 3875:Category 3568:Survival 3445:Johansen 3168:Binomial 3123:Isotonic 2710:(normal) 2355:location 2162:Blocking 2117:Sampling 1996:Q–Q plot 1961:Box plot 1943:Graphics 1838:Skewness 1828:Kurtosis 1800:Variance 1730:Heronian 1725:Harmonic 1532:See also 202:and the 3901:Commons 3848:Kriging 3733:Process 3690:studies 3549:Wavelet 3382:General 2549:Plug-in 2343:L space 2122:Cluster 1823:Moments 1641:Outline 452:may be 3770:Census 3360:Normal 3308:Manova 3128:Robust 2878:2-way 2870:1-way 2708:-test 2379:  1956:Biplot 1747:Median 1740:Lehmer 1682:Center 1589:  406:where 3394:Trend 2923:prior 2865:anova 2754:-test 2728:-test 2720:-test 2627:Power 2572:Pivot 2365:shape 2360:scale 1810:Shape 1790:Range 1735:Heinz 1710:Cubic 1646:Index 3627:Test 2827:Sign 2679:Wald 1752:Mode 1690:Mean 1587:ISBN 1489:and 483:are 2807:BIC 2802:AIC 37:In 3931:: 1528:. 721:. 491:, 2752:G 2726:F 2718:t 2706:Z 2425:V 2420:U 1622:e 1615:t 1608:v 1502:i 1475:i 1443:t 1439:X 1418:X 1392:i 1363:. 1358:i 1352:t 1342:i 1332:q 1327:1 1324:= 1321:i 1313:+ 1308:i 1302:t 1298:X 1292:i 1282:p 1277:1 1274:= 1271:i 1263:+ 1258:t 1250:+ 1247:c 1244:= 1239:t 1235:X 1209:t 1205:X 1181:. 1167:j 1140:i 1113:j 1097:; 1083:i 1079:Y 1056:j 1026:j 996:j 962:. 957:2 952:) 948:) 943:p 940:i 936:X 932:( 927:p 917:p 900:) 895:1 892:i 888:X 884:( 879:1 869:1 856:0 843:i 839:Y 834:( 827:n 822:1 819:= 816:i 808:= 803:2 798:i 788:n 783:1 780:= 777:i 769:= 766:S 741:j 707:j 679:, 676:) 673:n 670:, 664:, 661:1 658:= 655:i 652:( 648:) 643:p 640:i 636:X 632:( 627:p 617:p 609:+ 603:+ 600:) 595:1 592:i 588:X 584:( 579:1 569:1 561:+ 556:0 548:= 543:i 533:Y 504:j 469:i 438:p 430:, 424:, 419:1 391:n 388:, 382:, 379:1 376:= 373:i 367:i 359:+ 356:) 351:p 348:i 344:X 340:( 335:p 325:p 317:+ 311:+ 308:) 303:1 300:i 296:X 292:( 287:1 277:1 269:+ 264:0 256:= 251:i 247:Y 221:j 218:i 214:X 188:i 184:Y 163:n 160:, 154:, 151:1 148:= 145:i 141:, 138:) 133:p 130:i 126:X 122:, 116:, 111:1 108:i 104:X 100:, 95:i 91:Y 87:( 34:. 20:)

Index

Linear models
linear model of innovation
statistics
linearity
linear regression
time series analysis
statistical theory
Linear regression
statistical model
independent variables
nonlinear
random variables
regression coefficients
least squares
autoregressive moving average model
innovations
covariance
nonlinear dimensionality reduction
General linear model
Generalized linear model
Linear predictor function
Linear system
Linear regression
Statistical model
ISBN
0-12-564911-8
v
t
e
Statistics

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