The following is true for adjusted R square: Note: There is more than one correc
ID: 3204155 • Letter: T
Question
The following is true for adjusted R square:
Note: There is more than one correct answer.
1. It is a better indicator of fitness than R square in the case of multi variable regression.
2. It adjusts for the sample size and the number of independent variables used in the model.
3. It increases only when the additional variables included in the model are helpful in explaining the variation in the dependent variable.
4. Is a benchmark value for both single and mutli variable regressions.
5. It automatically adjusts for any typos in the data or software errors.
Please explain the concept to me if you can. Thank you!
Explanation / Answer
Answer:
. It is a better indicator of fitness than R square in the case of multi variable regression.
2. It adjusts for the sample size and the number of independent variables used in the model.
3. It increases only when the additional variables included in the model are helpful in explaining the variation in the dependent variable.
A note on Adjusted r^2:
Adjusted R^2, given by [1 - {(1 - R^2)(n - 1)/(n - p - 1)}] is a modification of R^2 that adjusts for the number of explanatory terms in a model. UnlikeR^2, the adjusted R^2increases only if the new term improves the model more than would be expected by chance alone. The adjusted R^2 can be negative, and will always be R^2. In the formula for R^2, p is the total number of regressors in the linear model , and n n is sample size. Unlike R^2, adjusted R^2 allows for the degrees of freedom associated with the sums of the squares. Therefore, even though the residual sum of squares decreases or remains the same as new explanatory variables are added, the residual variance does not. For this reason, adjusted R^2 is generally considered to be a more accurate measure of goodness-of-fit than R^2.
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