Part 1 I want to find the best linear model that predicts GPA based on 3 other v

Question

Part 1

I want to find the best linear model that predicts GPA based on 3 other variables from a collection of 15 variables. Some of these variables include SAT scores , ACT scores, teacher recommendation, etc. The number of models I would test is N=15 choose 3 = 455. The total error rate is 0.95 but I am still assuming that all tests are independent of each other. Can anyone explain why some tests might not be independent of each other?

What I think is that because the amount of tests are so large that there is likely to be some overlap between events.

Explanation / Answer

If there exists dependency between the variables then the tests may not be independent.suppose there are 4 variables A, B, C and D.Now let us assume that D is a result of C.i.e occurrence of D depends on the occurrence of C.Now if we consider the models (A, B, C) and (A, B, D) there will be a dependency in the models.

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