AIMs: Interpret the R^2 and adjusted-R^2 in a multiple regression. Define and discuss omitted variable bias in multiple regressions.
Questions:
223.1. Our multiple regression with four regressors returns a high R^2 of 0.72 and adjusted R^2 of 0.68. We add one regressor, for a total of five, and the OLS regression returns even an higher R^2 of 0.77 and adjusted R^2 of 0.71. We can draw the following four conclusion, each of which is true EXCEPT for:
a. We can conclude the additional (fifth) variable is significant
b. We cannot conclude causality; i.e., we cannot assume the regressors are a true cause of the dependent
c. We cannot conclude there is no omitted variable bias
d. We cannot know that we have the most appropriate set of regressors
223.2. A multiple regression with 165 observations (n = 165) on five regressors (k = 5) produces a standard error of the regression (SER) equal to 7.0 and a total sum of squares (TSS) equal to 26,000. What is the regression's adjusted R^2?
a. 0.33
b. 0.48
c. 0.69
d. 0.72
223.3. In a multiple regression, consider two things that might occur with respect to an omitted variable:
I. At least one of the included regressors must be correlated with the omitted variable.
II. The omitted variable must be a determinant of the dependent variable, Y.
In order for omitted variable bias to arise, which of the above must be true?
a. Neither are conditions
b. Only I. is a condition
c. Only II. is a condition
d. Both are conditions.
Answers:
Questions:
223.1. Our multiple regression with four regressors returns a high R^2 of 0.72 and adjusted R^2 of 0.68. We add one regressor, for a total of five, and the OLS regression returns even an higher R^2 of 0.77 and adjusted R^2 of 0.71. We can draw the following four conclusion, each of which is true EXCEPT for:
a. We can conclude the additional (fifth) variable is significant
b. We cannot conclude causality; i.e., we cannot assume the regressors are a true cause of the dependent
c. We cannot conclude there is no omitted variable bias
d. We cannot know that we have the most appropriate set of regressors
223.2. A multiple regression with 165 observations (n = 165) on five regressors (k = 5) produces a standard error of the regression (SER) equal to 7.0 and a total sum of squares (TSS) equal to 26,000. What is the regression's adjusted R^2?
a. 0.33
b. 0.48
c. 0.69
d. 0.72
223.3. In a multiple regression, consider two things that might occur with respect to an omitted variable:
I. At least one of the included regressors must be correlated with the omitted variable.
II. The omitted variable must be a determinant of the dependent variable, Y.
In order for omitted variable bias to arise, which of the above must be true?
a. Neither are conditions
b. Only I. is a condition
c. Only II. is a condition
d. Both are conditions.
Answers:
