Question

Using the lengths​ (in.), chest sizes​ (in.), and weights​ (lb) of bears from a data​ set, the resulting regression equation is Weight= - 274+0.426 Length +12.1 Chest Size. The​ P-value is 0.000 and the adjusted R^2 value is 0.925. If an additional predictor variable of neck size​ (in.) is​ included, the​ P-value becomes 0.000 and the adjusted R^2 becomes 0.933. Why is it better to use values of adjusted Rsquared instead of simply using values of R^2?
a. The unadjusted R^2 decreases or remains the same as more variables are included, but the adjusted R2 is adjusted for the number of variables and sample size.
b. The unadjusted R^2 can only be calculated for regression equations with two or fewer predictor variables, while the adjusted R2 can be calculated for regression equations with any number of predictor variables.
c. The unadjusted R^2 increases or remains the same as more variables are included, but the adjusted R2 is adjusted for the number of variables and sample size.
d. The unadjusted R^2 can only be calculated for regression equations with P-values greater than 0, while the adjusted R2 can be calculated for regression equations with any manner of P-value.

Answer 1

Answer:

C

Explanation:

Adjusted R^2 is calculated for multiple explanatory variables and R^2 value is calculated for only one explanatory variable.

Adjusted R^2 is always greater than R^2. As the sample size is increased or more variables are included, R^2 value increases and becomes closer to adjusted R^2 value. Adjusted R^2 value accounts for the number of variables and sample size