Interpreting linear regression coefficients for a covariate that's correlated with other covariatesNonlinear regression with correlated errorsWhat is correlated with what in a linear regression?Correlated explanatory variables in linear regressionInterpreting linear regression.Interpreting OLS Regression Coefficients with High MulticolinearityMarkov chains with nonlinear predictor variablesLinear Regression CoefficientsLinear regression with integer functionConsistent estimator for linear regression without interceptLinear Regression and Ridge Regression
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Interpreting linear regression coefficients for a covariate that's correlated with other covariates
Nonlinear regression with correlated errorsWhat is correlated with what in a linear regression?Correlated explanatory variables in linear regressionInterpreting linear regression.Interpreting OLS Regression Coefficients with High MulticolinearityMarkov chains with nonlinear predictor variablesLinear Regression CoefficientsLinear regression with integer functionConsistent estimator for linear regression without interceptLinear Regression and Ridge Regression
$begingroup$
The interpretation of linear regression coefficients that I learned is that the coefficient is the change in outcome associated with a unit change in that covariate, assuming all other covariates stay the same. But if the other covariates can't stay the same, can I somehow control for that?
In this example, where the covariates we have available are functions of the population model constituents (X1 and X2), an increase in covar2 is associated with an increase in the outcome. But covar2 will have a negative coefficient because of its correlation with covar1.
n <- 10000
X1 = runif(n, 0, 1)
X2 = rnorm(n, 1, 0.5)
error <- rnorm(n, 0, 0.1)
covar1 = 0.8*X1 + 0.4*X2
covar2 = 0.75*X1
Y = X1 + X2 + error
summary(lm(Y ~ covar1 + covar2))
The coefficients are
covar1 2.50
covar2 -1.33
But I don't know how to derive meaning from them because their covariates can't vary independently. Can I say something like "controlling for covar1, a unit increase in covar2 is associated with an increase of <some number> in the outcome."? If so, how would I derive <some number>?
regression linear-regression
asked yesterday
dgrogandgrogan
1012
$endgroup$
add a comment |
$begingroup$
The interpretation of linear regression coefficients that I learned is that the coefficient is the change in outcome associated with a unit change in that covariate, assuming all other covariates stay the same. But if the other covariates can't stay the same, can I somehow control for that?
In this example, where the covariates we have available are functions of the population model constituents (X1 and X2), an increase in covar2 is associated with an increase in the outcome. But covar2 will have a negative coefficient because of its correlation with covar1.
n <- 10000
X1 = runif(n, 0, 1)
X2 = rnorm(n, 1, 0.5)
error <- rnorm(n, 0, 0.1)
covar1 = 0.8*X1 + 0.4*X2
covar2 = 0.75*X1
Y = X1 + X2 + error
summary(lm(Y ~ covar1 + covar2))
The coefficients are
covar1 2.50
covar2 -1.33
But I don't know how to derive meaning from them because their covariates can't vary independently. Can I say something like "controlling for covar1, a unit increase in covar2 is associated with an increase of <some number> in the outcome."? If so, how would I derive <some number>?
regression linear-regression
asked yesterday
dgrogandgrogan
1012
$endgroup$
add a comment |
$begingroup$
The interpretation of linear regression coefficients that I learned is that the coefficient is the change in outcome associated with a unit change in that covariate, assuming all other covariates stay the same. But if the other covariates can't stay the same, can I somehow control for that?
In this example, where the covariates we have available are functions of the population model constituents (X1 and X2), an increase in covar2 is associated with an increase in the outcome. But covar2 will have a negative coefficient because of its correlation with covar1.
n <- 10000
X1 = runif(n, 0, 1)
X2 = rnorm(n, 1, 0.5)
error <- rnorm(n, 0, 0.1)
covar1 = 0.8*X1 + 0.4*X2
covar2 = 0.75*X1
Y = X1 + X2 + error
summary(lm(Y ~ covar1 + covar2))
The coefficients are
covar1 2.50
covar2 -1.33
But I don't know how to derive meaning from them because their covariates can't vary independently. Can I say something like "controlling for covar1, a unit increase in covar2 is associated with an increase of <some number> in the outcome."? If so, how would I derive <some number>?
regression linear-regression
asked yesterday
dgrogandgrogan
1012
$endgroup$
The interpretation of linear regression coefficients that I learned is that the coefficient is the change in outcome associated with a unit change in that covariate, assuming all other covariates stay the same. But if the other covariates can't stay the same, can I somehow control for that?
In this example, where the covariates we have available are functions of the population model constituents (X1 and X2), an increase in covar2 is associated with an increase in the outcome. But covar2 will have a negative coefficient because of its correlation with covar1.
n <- 10000
X1 = runif(n, 0, 1)
X2 = rnorm(n, 1, 0.5)
error <- rnorm(n, 0, 0.1)
covar1 = 0.8*X1 + 0.4*X2
covar2 = 0.75*X1
Y = X1 + X2 + error
summary(lm(Y ~ covar1 + covar2))
The coefficients are
covar1 2.50
covar2 -1.33
But I don't know how to derive meaning from them because their covariates can't vary independently. Can I say something like "controlling for covar1, a unit increase in covar2 is associated with an increase of <some number> in the outcome."? If so, how would I derive <some number>?
regression linear-regression
regression linear-regression
asked yesterday
dgrogandgrogan
1012
asked yesterday
dgrogandgrogan
1012
asked yesterday
dgrogandgrogan
1012
asked yesterday
dgrogandgrogan
1012
asked yesterday
dgrogandgrogan
1012
1012
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
When you make inference in regression analysis regarding the effect of an independent variable on the dependent, you usually (always) presume ceteris paribus, namely, when any other covariate remains unchanged (i.e., an analogue to partial derivative in calculus)
https://en.wikipedia.org/wiki/Ceteris_paribus#Economics.
And "some number" is the coefficient, i.e., for the first covariate is $2.5$.
answered yesterday
V. VancakV. Vancak
11.3k2926
$endgroup$
$begingroup$
What do you do when you know another covariate does not remain unchanged?
$endgroup$
– dgrogan
20 hours ago
add a comment |
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1 Answer
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1 Answer
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active
oldest
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$begingroup$
When you make inference in regression analysis regarding the effect of an independent variable on the dependent, you usually (always) presume ceteris paribus, namely, when any other covariate remains unchanged (i.e., an analogue to partial derivative in calculus)
https://en.wikipedia.org/wiki/Ceteris_paribus#Economics.
And "some number" is the coefficient, i.e., for the first covariate is $2.5$.
answered yesterday
V. VancakV. Vancak
11.3k2926
$endgroup$
$begingroup$
What do you do when you know another covariate does not remain unchanged?
$endgroup$
– dgrogan
20 hours ago
add a comment |
$begingroup$
When you make inference in regression analysis regarding the effect of an independent variable on the dependent, you usually (always) presume ceteris paribus, namely, when any other covariate remains unchanged (i.e., an analogue to partial derivative in calculus)
https://en.wikipedia.org/wiki/Ceteris_paribus#Economics.
And "some number" is the coefficient, i.e., for the first covariate is $2.5$.
answered yesterday
V. VancakV. Vancak
11.3k2926
$endgroup$
$begingroup$
What do you do when you know another covariate does not remain unchanged?
$endgroup$
– dgrogan
20 hours ago
add a comment |
$begingroup$
When you make inference in regression analysis regarding the effect of an independent variable on the dependent, you usually (always) presume ceteris paribus, namely, when any other covariate remains unchanged (i.e., an analogue to partial derivative in calculus)
https://en.wikipedia.org/wiki/Ceteris_paribus#Economics.
And "some number" is the coefficient, i.e., for the first covariate is $2.5$.
answered yesterday
V. VancakV. Vancak
11.3k2926
$endgroup$
When you make inference in regression analysis regarding the effect of an independent variable on the dependent, you usually (always) presume ceteris paribus, namely, when any other covariate remains unchanged (i.e., an analogue to partial derivative in calculus)
https://en.wikipedia.org/wiki/Ceteris_paribus#Economics.
And "some number" is the coefficient, i.e., for the first covariate is $2.5$.
answered yesterday
V. VancakV. Vancak
11.3k2926
answered yesterday
V. VancakV. Vancak
11.3k2926
answered yesterday
V. VancakV. Vancak
11.3k2926
answered yesterday
V. VancakV. Vancak
11.3k2926
11.3k2926
$begingroup$
What do you do when you know another covariate does not remain unchanged?
$endgroup$
– dgrogan
20 hours ago
add a comment |
$begingroup$
What do you do when you know another covariate does not remain unchanged?
$endgroup$
– dgrogan
20 hours ago
$begingroup$
What do you do when you know another covariate does not remain unchanged?
$endgroup$
– dgrogan
20 hours ago
$begingroup$
What do you do when you know another covariate does not remain unchanged?
$endgroup$
– dgrogan
20 hours ago
add a comment |
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