Impossible exam problem! (regression analysis)
This may not be the most appropriate forum for posting exam problems, but in doing so I hope to learn from the solution. In this case though I don't think there's a solution to the question I just had on one of my exams.
1. Use the following information to determine the most appropriate model by the R^2 method. (he is referring to the method where you look at the R^2 value of the regression for each combination of predictor variables, from no predictors up to the full model, picking the best model for the 1 predictor model, 2 predictor model.... and then determining if the R^2 of a reduced model is close enough to the value of the full model that you can go with the reduced model instead).
Info given is following....
model: y = b0 + b1x1 + b2x2 + b3x3
n = 25
then we are given the residual sum of squares for the models with each combination of predictors (that is: no predictors, x1, x2, x3, x1 x2, x1 x3, x2 x3, x1 x2 x3).
so the obvious thing to do is divide each residual sum of squares value by (n-p) to get your s^2 value, then choose the model with the lowest s^2 value. BUT... that's not what he asked for. He asked us to use the R^2 method, not the s^2 method. So the real point of the problem is to see if we can get the R^2 values when we are only given 1) SSresidual 2) n 3) p 4) s^2
I don't think it can be done.