edj24Homework6 Word iew View HelpO Tell me what you want to do 1Normal 1 No Spac
ID: 3075326 • Letter: E
Question
edj24Homework6 Word iew View HelpO Tell me what you want to do 1Normal 1 No Spac.. Heading 1 Heading 2 Title Subtitle Paragraph Styles (10+ 6x5-40 points) a) Fill in the blanks in the following tables. The column labeled "Seq SS" represents "sequential sums of squares" (measures the reduction in the SS when a term is added to a model that contains only the terms before it), while the column labeled "Adj SS" represents "adjusted sums of squares" (measures the reduction in the SS for each term relative to a model that contains all of the remaining terms). [Hint: The t-statistics in the Coefficients table assume all other predictors are included in the model, so if we square these we get the F-statistics in the ANOVA table based on Adjusted Sums of Squares.] f Seq Ss Adj SSF-statistic Source p-value based on Adj SS based on Adj SS Regression 3 8208.9 82089 39.38 X1 X2 X3 Error 1 5453.41772. 12551.7 2560.01 36.84 1203.8 203.8 93 6462.6 6462.6 0.000 0.000 0.000 0.090 25.50 2.93 Total 96 146715 146715 Coefficients Se Soef tststic value Term Constant X1 X2 X3 15.71 2.638 0.5108 0.0106 4.60 0.522 0.0842 0.00620 3.42 5.05 6.07 1.71 p-value 0.001 0.000 0.000 0.090 b) Calculate SSR(X31%), that is the sequential sum of squares obtained by adding X3 to a model already containing only the predictor Xi. Show your work.Explanation / Answer
a) It is already solved in the question
b) The sequential sum of squares tells us how much the SSE declines after we add another variable to the model that contains only the variables preceding it. By contrast, the adjusted sum of squares tells us how much the SSE declines after we add another variable to the model that contains every other variable.
So if you start with zero predictors and add X1, SS Regression increases by 5434.4. Then if you also add X3, the SS Regression increases by an additional 203.8. These are the sequential SS, which add up to the total SS Regression of 8208.9 if you add X2 too.
Thus we can say SSR(X3|X1) = 203.8
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