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.]
Source df Seq SS Adj SS F-statistic
based on Adj SS p-value
based on Adj SS
Regression 3 100.866 35.14 0.000
X1 1 67.444 33.031 34.52 0.000
X2 1 3.883
X3 1 30.88 0.000
Error 93 ---- -------
Total 96 189.842 189.842 ---- -------
Coefficients
Term Coef SE coef t-statistic p-value
Constant 0.58 1.24 0.45 0.652
X1 0.34 0.058 5.88 0.000
X2 -0.01 0.0245
X3 0.06 0.0103 5.56 0.000
b) Calculate SSR(X3|X1), that is the sequential sum of squares obtained by adding X3 to a model already containing only the predictor X1. Show your work.
c) Calculate the value of an F-statistic for testing H0: β2 = β3 = 0 within the model Yi = β0 + β1 Xi,1 + β2 Xi,2 + β3 Xi,3 + εi. It is not necessary to carry out the test - just calculate the value of F. Show your work.
d) Calculate the value of the coefficient of partial determination R2Y,2|1.