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008 009 004 005 00 007 0002 C002 0002 000 000 0002 0003 0003 0003 0003 0003 0 Pa

ID: 3052373 • Letter: 0

Question

008 009 004 005 00 007 0002 C002 0002 000 000 0002 0003 0003 0003 0003 0003 0 Part II. Written Problems Question 1 (10 points): Describe the procedure of using utility test and individual test to select predictors. Suppose you have a data with one response variable, and three independent variables. (Perhaps math notation can be used, but no math proof required here) Question 2 (15 points): Explain the concept of least squares estimation. Support your explanation by sketching an x-y axis and some data points. Specifically, what quantity is minimized by the least squares line? 2-3 sentences should be enough. (No math proof required here

Explanation / Answer

1)

F test:

ho: model is significant

h1: model is significant

F = MSR/MSE with df1=k ; df2= n-k-1

if p-value < alpha, i reject ho at alpha% level of significance and conclude that model is significant

individual testing

Hypothesis test of slope

Null Hypothesis: Hoi: i=0, i is not significant, i.e. Xi should be included in the model. V/s Alternative Hypothesis: H1i: i0, i is significant, i.e. Xi should not be included in the model. If p-value < alpha, I reject Hoi at 5% level of significance otherwise I fail to reject it.