Multiple Linear Regression: A) Multiple linear regression allows for the effect
ID: 3221844 • Letter: M
Question
Multiple Linear Regression: A) Multiple linear regression allows for the effect of potential confounding variables to be controlled for in the analysis of a relationship between X and Y (T or F)? B) If researchers want to assume that X1 is the explanatory variable in a linear model Y=+1*X1+2*X2+3*X3, and then decide that they want to observe the relationship as though X2 were the explanatory variable, they must re-work the model and compute new beta coefficients (T or F)? C) Deviations away from the diagonal line presented in a normal Q-Q plot output indicate a high R2 value, and thus a proper approximation by the multiple linear regression model (T or F)?
Explanation / Answer
A) The statement is true.
In multiple linear regression, we are able to include all potential variables, that we can imagine to affect the variable under study (dependent variable), as regressors. Therefore, we have an opportunity to quantify the effects of all potential cofounding variables, thereby controlling their effect in analyzing the relationship between X and Y. As a result, these variables are no longer confounding variables and they are part of the study itself.
B) The statement is false.
If a linear model is of the form Y=+1*X1+2*X2+3*X3, then the researcher is considering the three variables X1, X2 and X3 as explanatory variables, as opposed to considering any one of the variables as the only explanatory variable. Therefore, there is no need to re-work the model because all the explanatory variables have already been considered.
C) The statement is false.
I am assuming that the Q-Q plot is drawn between the observed values of the dependent variable and the values of the dependent variable predicted by the regression model. If the Q-Q plot deviates away from the diagonal line presented in the normal Q-Q plot, it indicates that the regression model has not done a good job in predicting the values of the dependent variable. In other words, the R2 of the model is low.
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