20. Which of the following is correct in a multiple linear regression? Choose al

Question

20. Which of the following is correct in a multiple linear regression? Choose all correct answers.

a. Using Type I sums of squares, the order that variables enter into the model is not important.

b. In order to perform a multiple partial f-test, both Type I and Type III sums of squares are needed.

c. A test for the significance of each variable as it enters the model uses Type III sums of squares.

d. A test for the significance of each variable as added last to the model uses Type I sums of squares.

e. Both Type I sums of squares and Type III sums of squares produce the same sum of squares error.

Explanation / Answer

suppose that you wish to test the hypothesis that pp coefficients are zero, and thus these variables can be omitted from the model, and you also have kk coefficients in the full model(including the intercept). The test is based on the comparison of the Residual Sum of Squares(RSS) and thus you need to run two separate regressions and save the RSS from each one. For the full model the RSS will be lower since the addition of new vabiables invariably leads to a reduction of the RSS (and an increase in the Explained Sum of Squares, this is closely related to R2R2). What we are testing therefore is whether the difference is so large that the removal of the variables will be detrimental to the model. Let's be a little more specific. The test takes the following form

F=RSSReducedRSSFullpRSSFullnkF=RSSReducedRSSFullpRSSFullnk

option E is correct

In ANOVA, when the data are balanced (equal cell sizes) the factors are orthogonal and all three types of sums of squares are identical (). Orthogonal, or independent, indicates that there is no variance shared across the various effects, and the separate sums of squares can be added to obtain the model sums of squares. This is a key point in the mystery of the differing results in PROC GLM and PROC REG. Recall that the design was balanced – the cell sizes were all 28, and in PROC GLM the Type I and Type III sums of squares were identical as one would expect with an orthogonal design

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