Lesson 6 Problem Complete Solution

Question: #8944

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.

Solution: #8972

Lesson 6 Problem Complete Solution

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. S...