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.