PLEASE HELP ME ANSWER THOSE QUESTIONS (2 pts) You are using the Cp criterion to

Question

PLEASE HELP ME ANSWER THOSE QUESTIONS

(2 pts) You are using the Cp criterion to select a subset of explanatory variables in a multiple regression. The best subset of size 3 gives Cp 8. Interpret this result. (2 pts) In a one-way ANOVA with three groups, you are interested in the difference twice the mean of the first group and the sum of the means of the other two groups. If the MSE is 50, and the sample sizes are 15, 6, and 15, find the standard error for this difference. (Specify the contrast you use.

Explanation / Answer

(first part) here P=3 and Cp=8 which means subset is not best . As the Cp should lie between P and 2P.

Mallows' Cp can help you choose between competing multiple regression models. Mallows' Cp compares the full model to models with the best subsets of predictors. It helps you strike an important balance with the number of predictors in the model. A model with too many predictors can be relatively imprecise while a model with too few predictors can produce biased estimates. Using Mallows' Cp to compare regression models is only valid when you start with the same complete set of predictors. Under a model not suffering from appreciable lack of fit (bias), Cp has expectation nearly equal to P ( number of parameter in subset); otherwise the expectation is roughly P plus a positive bias term.  In practice, the positive bias can be adjusted for by selecting a model from the ordered list of subsets, such that Cp < 2P.

(second part) here total df=36-1=35,

between group df=3-1=2

within group df=35-2=33

Standard Error(SE)=sqrt(2*MSE*(1/r1+1/r2))

SE(1st and 2nd)=sqrt(2*50((1/15 + 1/6))=4.83

SE(2nd and 3rd)=sqrt(2*50((1/6 + 1/15))=4.83

SE(1st and 3rd)=sqrt(2*50((1/15 + 1/15))=3.65

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