Schweser Book 1 Page 187: “Whenever there is more than one independent variable, R^2a is less than or equal to R^2.” And they give this question: In regard to multiple regression analysis, which of the following statements is most accurate? A) Adjusted R2 always decreases as independent variables increase. B) R2 is less than adjusted R2. C) Adjusted R2 is less than R2. Your answer: C was correct! Whenever there is more than one independent variable, adjusted R2 is less than R2. Adding a new independent variable will increase R2, but may either increase or decrease adjusted R2.
If anyone’s interested i looked it up in CFAI books. "Note that if k >= 1, then R^2 is strictly greater than adjusted R^2.’ So I guess since k is always >= 1, R^2 is always greater and the two are never equal. Schweser is wrong.
Schweser isn’t wrong. R^2 is always greater than aR^2. The degree of difference is what changes as more independent variables are added.
you’re right that the degree of difference increase as more independent variables are added. what im referring to as wrong in schweser is the sentence “Whenever there is more than one independent variable, R^2a is less than or equal to R^2.” The reason is because CFAI says that “R^2 is strictly greater than adjusted R^2.” as long as you have one more more independevt variables.
Wow, nice pickup. I had thought that it was possible for aR^2 to equal R^2, but I guess not.