846:. Here the dependent variable (and variable of most interest) was the annual mean sea level at a given location for which a series of yearly values were available. The primary independent variable was time. Use was made of a covariate consisting of yearly values of annual mean atmospheric pressure at sea level. The results showed that inclusion of the covariate allowed improved estimates of the trend against time to be obtained, compared to analyses which omitted the covariate.
101:
832:"Explanatory variable" is preferred by some authors over "independent variable" when the quantities treated as independent variables may not be statistically independent or independently manipulable by the researcher. If the independent variable is referred to as an "explanatory variable" then the term "response variable" is preferred by some authors for the dependent variable.
839:"Explained variable" is preferred by some authors over "dependent variable" when the quantities treated as "dependent variables" may not be statistically dependent. If the dependent variable is referred to as an "explained variable" then the term "predictor variable" is preferred by some authors for the independent variable.
957:
under examination. For example, in a study examining the effect of post-secondary education on lifetime earnings, some extraneous variables might be gender, ethnicity, social class, genetics, intelligence, age, and so forth. A variable is extraneous only when it can be assumed (or shown) to influence
933:
A variable may be thought to alter the dependent or independent variables, but may not actually be the focus of the experiment. So that the variable will be kept constant or monitored to try to minimize its effect on the experiment. Such variables may be designated as either a "controlled variable",
1050:
In a study measuring the influence of different quantities of fertilizer on plant growth, the independent variable would be the amount of fertilizer used. The dependent variable would be the growth in height or mass of the plant. The controlled variables would be the type of plant, the type of
835:
Depending on the context, a dependent variable is sometimes called a "response variable", "regressand", "criterion", "predicted variable", "measured variable", "explained variable", "experimental variable", "responding variable", "outcome variable", "output variable", "target" or "label". In
1061:
In a study of how different doses of a drug affect the severity of symptoms, a researcher could compare the frequency and intensity of symptoms when different doses are administered. Here the independent variable is the dose and the dependent variable is the frequency/intensity of
996:
Situational variables are features of the environment in which the study or research was conducted, which have a bearing on the outcome of the experiment in a negative way. Included are the air temperature, level of activity, lighting, and time of
992:
Blocking variables or experimental variables are characteristics of the persons conducting the experiment which might influence how a person behaves. Gender, the presence of racial discrimination, language, or other factors may qualify as such
92:
test the effects that the independent variables have on the dependent variables. Sometimes, even if their influence is not of direct interest, independent variables may be included for other reasons, such as to account for their potential
750:, the variable manipulated by an experimenter is something that is proven to work, called an independent variable. The dependent variable is the event expected to change when the independent variable is manipulated.
49:), on the values of other variables. Independent variables, in turn, are not seen as depending on any other variable in the scope of the experiment in question. In this sense, some common independent variables are
712:
1319:
801:
Depending on the context, an independent variable is sometimes called a "predictor variable", "regressor", "covariate", "manipulated variable", "explanatory variable", "exposure variable" (see
145:
is a rule for taking an input (in the simplest case, a number or set of numbers) and providing an output (which may also be a number). A symbol that stands for an arbitrary input is called an
989:
Subject variables, which are the characteristics of the individuals being studied that might affect their actions. These variables include age, gender, health status, mood, background, etc.
1072:
In measuring the amount of color removed from beetroot samples at different temperatures, temperature is the independent variable and amount of pigment removed is the dependent variable.
1605:
2000:
2005:
1868:
1026:
1995:
1316:
84:
context. In an experiment, any variable that can be attributed a value without attributing a value to any other variable is called an independent variable.
1598:
503:
are independent random variables. This occurs when the measurements do not influence each other. Through propagation of independence, the independence of
2127:
1655:
1082:
The taste varies with the amount of sugar added in the coffee. Here, the sugar is the independent variable, while the taste is the dependent variable.
1768:
1812:
1591:
1706:
1575:
1425:
1990:
1400:
69:, and previous values of some observed value of interest (e.g. human population size) to predict future values (the dependent variable).
1915:
1194:
Hastings, Nancy Baxter. Workshop calculus: guided exploration with review. Vol. 2. Springer
Science & Business Media, 1998. p. 31
2122:
1701:
1665:
1556:
1533:
1475:
1450:
1374:
1348:
1304:
1260:
568:
28:
1763:
1675:
1731:
1102:
2046:
1802:
2112:
1645:
1817:
1660:
1650:
319:
is known as the "error" and contains the variability of the dependent variable not explained by the independent variable.
2117:
1670:
1640:
1905:
1900:
1775:
1736:
45:. Dependent variables are studied under the supposition or demand that they depend, by some law or rule (e.g., by a
1227:
Anton, Howard, Irl C. Bivens, and
Stephen Davis. Calculus Single Variable. John Wiley & Sons, 2012. Section 0.1
814:
1945:
2081:
2051:
2026:
1125:
when it exists), the nomenclature is kept if the inverse dependency is not the object of study in the experiment.
1940:
1950:
1920:
1910:
1807:
758:
225:
982:; in these situations, design changes and/or controlling for a variable statistical control is necessary.
184:
142:
109:
2066:
2061:
1955:
1879:
1858:
1726:
1721:
1716:
1711:
1635:
1614:
1097:
1092:
979:
747:
237:
183:
It is possible to have multiple independent variables or multiple dependent variables. For instance, in
46:
974:
the regression's result for the effect of that independent variable of interest. This effect is called
240:, the relationship between the set of dependent variables and set of independent variables is studied.
1960:
1884:
1853:
1500:
1033:
1029:
66:
1970:
1863:
1757:
942:
822:
790:
113:
2091:
1930:
1925:
1848:
1680:
1162:
959:
810:
802:
1571:
1552:
1529:
1471:
1446:
1421:
1396:
1370:
1344:
1300:
1266:
1256:
971:
379:
2076:
2056:
1508:
1122:
945:
as independent variables, may aid a researcher with accurate response parameter estimation,
935:
818:
762:
85:
1004:
1001:
In modelling, variability that is not covered by the independent variable is designated by
2036:
1965:
1323:
1283:
950:
117:
2041:
1504:
2031:
1838:
1388:
718:
2106:
963:
121:
224:
are independent variables. Functions with multiple outputs are often referred to as
17:
2086:
2021:
1935:
826:
383:
247:
785:. Known values for the target variable are provided for the training data set and
1206:
Carlson, Robert. A concrete introduction to real analysis. CRC Press, 2006. p.183
1843:
975:
806:
754:
94:
34:
Concept in mathematical modeling, statistical modeling and experimental sciences
2071:
1741:
1512:
1327:
1253:
A modern introduction to probability and statistics: understanding why and how
1236:
Larson, Ron, and Bruce
Edwards. Calculus. Cengage Learning, 2009. Section 13.1
967:
954:
946:
244:
89:
81:
73:
1420:(Fifth ed.). Mason, OH: South-Western Cengage Learning. pp. 22â23.
1270:
1051:
fertilizer, the amount of sunlight the plant gets, the size of the pots, etc.
970:
with one or more of the independent variables of interest, its omission will
1833:
1036:", "unexplained share", "residual variable", "disturbance", or "tolerance".
789:
set, but should be predicted for other data. The target variable is used in
786:
100:
1873:
1583:
105:
1570:
Ash
Narayan Sah (2009) Data Analysis Using Microsoft Excel, New Delhi.
58:
829:, the term "control variable" is usually used instead of "covariate".
1121:
Even if the existing dependency is invertible (e.g., by finding the
394:
as the dependent variable. This is also called a bivariate dataset,
1395:(Fifth international ed.). New York: McGraw-Hill. p. 21.
836:
economics endogenous variables are usually referencing the target.
99:
54:
966:. If it is excluded from the regression and if it has a non-zero
149:, while a symbol that stands for an arbitrary output is called a
842:
An example is provided by the analysis of trend in sea level by
62:
50:
1587:
1528:
Everitt, B.S. (2002) Cambridge
Dictionary of Statistics, CUP.
1180:
Alligood, Kathleen T.; Sauer, Tim D.; Yorke, James A. (1996).
707:{\displaystyle E=E=\alpha +\beta x_{i}+E=\alpha +\beta x_{i}.}
1218:
Stewart, James. Calculus. Cengage
Learning, 2011. Section 1.1
985:
Extraneous variables are often classified into three types:
781:), while an independent variable may be assigned a role as
1491:
Woodworth, P. L. (1987). "Trends in U.K. mean sea level".
444:. The simple linear regression model takes the form of
124:
representing the dependent variable. In this function,
72:
Of the two, it is always the dependent variable whose
1007:
743:
correspond to the intercept and slope, respectively.
571:
76:
is being studied, by altering inputs, also known as
27:
For dependent and independent random variables, see
2014:
1983:
1893:
1826:
1795:
1788:
1750:
1689:
1628:
1621:
1361:
1359:
1357:
1020:
962:. If included in a regression, it can improve the
706:
322:With multiple independent variables, the model is
2001:List of nonlinear ordinary differential equations
2006:List of nonlinear partial differential equations
547:has an expectation value of 0 and a variance of
308:th value of the independent variable. The term
159:, and the most common symbol for the output is
1996:List of linear ordinary differential equations
120:representing the independent variable and the
1599:
1297:Random House Webster's Unabridged Dictionary.
953:, but are not of substantive interest to the
793:algorithms but not in unsupervised learning.
187:, one often encounters functions of the form
8:
1418:Introductory Econometrics: A Modern Approach
1524:
1522:
1792:
1625:
1606:
1592:
1584:
1549:The Oxford Dictionary of Statistical Terms
1367:The Oxford Dictionary of Statistical Terms
1341:The Oxford Dictionary of Statistical Terms
1246:
1244:
1242:
1182:Chaos an introduction to dynamical systems
1056:Effect of drug dosage on symptom severity:
165:; the function itself is commonly written
153:. The most common symbol for the input is
1543:
1541:
1214:
1212:
1202:
1200:
1012:
1006:
843:
695:
670:
651:
626:
613:
582:
570:
1566:
1564:
1299:Random House, Inc. 2001. Page 534, 971.
848:
765:), the dependent variable is assigned a
536:has a different expectation value. Each
375:is the number of independent variables.
1138:
1114:
941:Extraneous variables, if included in a
293:th value of the dependent variable and
1468:The Cambridge Dictionary of Statistics
1067:Effect of temperature on pigmentation:
1045:Effect of fertilizer on plant growths:
7:
1991:List of named differential equations
1391:(2009). "Terminology and Notation".
378:In statistics, more specifically in
1916:Method of undetermined coefficients
1697:Dependent and independent variables
735:and is called the regression line.
1351:(entry for "independent variable")
1077:Effect of sugar added in a coffee:
25:
2128:Independence (probability theory)
1251:Dekking, Frederik Michel (2005),
1167:Elementary differential equations
1148:Mathematical modelling techniques
29:Independence (probability theory)
1813:Carathéodory's existence theorem
390:as the independent variable and
1103:Latent and observable variables
1470:(2nd ed.). Cambridge UP.
1445:(Fourth ed.). Oxford UP.
676:
663:
632:
597:
588:
575:
128:is the dependent variable and
1:
717:The line of best fit for the
1641:Notation for differentiation
1443:A Dictionary of Epidemiology
1416:Wooldridge, Jeffrey (2012).
212:is a dependent variable and
132:is the independent variable.
1737:Exact differential equation
1441:Last, John M., ed. (2001).
2144:
1317:English Manual version 1.0
825:) or "input variable". In
386:of data is generated with
232:In modeling and statistics
26:
2047:JĂłzef Maria Hoene-WroĆski
2027:Gottfried Wilhelm Leibniz
1818:CauchyâKowalevski theorem
1513:10.1080/15210608709379549
1146:Aris, Rutherford (1994).
37:A variable is considered
2123:Mathematical terminology
1941:Finite difference method
1377:(entry for "regression")
1169:. John Wiley & Sons.
938:", or "fixed variable".
514:implies independence of
1921:Variation of parameters
1911:Separation of variables
1808:Peano existence theorem
1803:PicardâLindelöf theorem
1690:Attributes of variables
1466:Everitt, B. S. (2002).
759:multivariate statistics
226:vector-valued functions
2082:Carl David Tolmé Runge
1656:Differential-algebraic
1615:Differential equations
1387:Gujarati, Damodar N.;
1150:. Courier Corporation.
1022:
708:
185:multivariable calculus
133:
2113:Design of experiments
2067:Augustin-Louis Cauchy
2062:Joseph-Louis Lagrange
1956:Finite element method
1946:CrankâNicolson method
1880:Numerical integration
1859:Exponential stability
1751:Relation to processes
1636:Differential operator
1098:Blocking (statistics)
1093:Abscissa and ordinate
1028:and is known as the "
1023:
1021:{\displaystyle e_{I}}
980:omitted variable bias
777:(or in some tools as
709:
238:mathematical modeling
103:
47:mathematical function
1961:Finite volume method
1885:Dirac delta function
1854:Asymptotic stability
1796:Existence/uniqueness
1661:Integro-differential
1184:. Springer New York.
1005:
569:
147:independent variable
43:independent variable
41:if it depends on an
18:Independent variable
2118:Regression analysis
1971:Perturbation theory
1951:RungeâKutta methods
1931:Integral transforms
1864:Rate of convergence
1760:(discrete analogue)
1505:1987MarGe..11...57W
1161:Boyce, William E.;
1032:", "side effect", "
943:regression analysis
851:
823:pattern recognition
791:supervised learning
525:, even though each
137:In pure mathematics
104:In single variable
2092:Sofya Kovalevskaya
1926:Integrating factor
1849:Lyapunov stability
1769:Stochastic partial
1393:Basic Econometrics
1330:5.0, October 2013.
1322:2014-02-10 at the
1163:Richard C. DiPrima
1018:
960:dependent variable
849:
811:medical statistics
803:reliability theory
704:
151:dependent variable
141:In mathematics, a
134:
2100:
2099:
1979:
1978:
1784:
1783:
1576:978-81-7446-716-4
1547:Dodge, Y. (2003)
1427:978-1-111-53104-1
1365:Dodge, Y. (2003)
1339:Dodge, Y. (2003)
926:
925:
719:bivariate dataset
551:. Expectation of
380:linear regression
16:(Redirected from
2135:
2077:Phyllis Nicolson
2057:Rudolf Lipschitz
1894:Solution methods
1869:Series solutions
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1402:978-007-127625-2
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1123:inverse function
1119:
1027:
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1024:
1019:
1017:
1016:
964:fit of the model
936:control variable
922:label or target
852:
844:Woodworth (1987)
819:machine learning
783:regular variable
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763:machine learning
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2102:
2101:
2096:
2037:Jacob Bernoulli
2010:
1975:
1966:Galerkin method
1889:
1827:Solution topics
1822:
1780:
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1389:Porter, Dawn C.
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1324:Wayback Machine
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951:goodness of fit
931:
929:Other variables
799:
779:label attribute
773:target variable
772:
771:
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736:
722:
721:takes the form
691:
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67:fluid flow rate
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2032:Leonhard Euler
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2015:Mathematicians
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1742:On jet bundles
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1707:Nonhomogeneous
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1622:Classification
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1493:Marine Geodesy
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850:Antonym pairs
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478:= 1, 2, ... ,
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243:In the simple
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24:
14:
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9:
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3:
2:
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231:
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216:
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191:
186:
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173:
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152:
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122:vertical axis
119:
115:
112:is typically
111:
107:
102:
98:
96:
91:
87:
83:
79:
75:
70:
68:
64:
60:
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52:
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40:
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19:
2087:Martin Kutta
2042:Ămile Picard
2022:Isaac Newton
1936:Euler method
1906:Substitution
1696:
1548:
1499:(1): 57â87.
1496:
1492:
1486:
1467:
1461:
1442:
1436:
1417:
1411:
1392:
1382:
1366:
1340:
1335:
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1252:
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1190:
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1147:
1141:
1117:
1000:
984:
940:
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838:
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827:econometrics
800:
782:
778:
770:
766:
752:
745:
731:
727:
723:
716:
557:
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538:
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384:scatter plot
377:
371:
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343:
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328:
324:
321:
314:
310:
299:
295:
284:
280:
273:
269:
264:
260:
255:
251:
248:linear model
242:
235:
220:
214:
208:
201:
197:
193:
189:
182:
175:
171:
167:
161:
155:
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1844:Phase space
1702:Homogeneous
1284:"Variables"
976:confounding
903:manipulated
898:endogenous
887:explanatory
874:regressand
855:independent
807:risk factor
757:tools (for
755:data mining
95:confounding
90:experiments
82:statistical
2107:Categories
2072:John Crank
1901:Inspection
1764:Stochastic
1758:Difference
1732:Autonomous
1676:Non-linear
1666:Fractional
1629:Operations
1328:RapidMiner
1133:References
993:variables.
968:covariance
955:hypothesis
947:prediction
890:explained
882:predicted
858:dependent
748:experiment
245:stochastic
78:regressors
1876:solutions
1834:Wronskian
1789:Solutions
1717:Decoupled
1681:Holonomic
1271:783259968
1062:symptoms.
906:measured
895:exogenous
879:predictor
871:regressor
787:test data
689:β
683:α
645:β
639:α
607:β
601:α
352:+ ... + b
278:the term
116:with the
74:variation
39:dependent
1984:Examples
1874:Integral
1646:Ordinary
1320:Archived
1165:(2012).
1087:See also
1040:Examples
1030:residual
919:feature
914:outcome
911:exposure
797:Synonyms
369:, where
206:, where
143:function
110:function
106:calculus
97:effect.
1712:Coupled
1651:Partial
1551:, OUP.
1501:Bibcode
1369:, OUP.
1343:, OUP.
866:output
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493:, ... ,
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289:is the
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1727:Degree
1671:Linear
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86:Models
1776:Delay
1722:Order
1109:Notes
1034:error
863:input
80:in a
55:space
1572:ISBN
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1371:ISBN
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1301:ISBN
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767:role
761:and
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