Question

Suppose we are working on the same data set. Two multiple linear regressions have been done with following

Printout, where “ “ means blank space.

Analysis of Variance Table 1

Response: y

                Df                Sum Sq            Mean Sq          F value             Pr(>F)

x1               1               ---------             ----------           --------      ------------- ***

x2               1               80.206             80.206             17.892    0.0001474 ***

Residuals 37               165.864                        4.483

Analysis of Variance Table 2

Response: y

                        Df        Sum Sq            Mean Sq          F value             Pr(>F)

x1                      1       ---------             -----------          --------    --------------- ***

x2                       1       80.206             80.206             1563.7 <     2.2e-16 ***

x3                       1       ---------             -----------          --------    ---------------

Residuals         36       1.847             0.051

a. How many observations we have in the data set?

b. Clearly the ANOVA Table 2 is associated with the regression model:

E[y|x]= β₀+β₁x1+β₂x₂+ β₃x₃. Suppose you want to test H₀: β₃=0. Please carry out an F-test?

c. For the model

E[y|x]= β₀+β₁x1+β₂x₂+ β₃x₃

Suppose you want to test H0: β₁= β₃=0.In order to carry out an F-test for that, what is the other regression

ANOVA table we need?

Answer 1

This question is mostly illegible, but i will still try to answer.

a.

b.

c.

You need the value of SS(X1) in order to carry out the F-test. If Total Sum Of Squares are given you could also use that to calculate SS(X1) and carry out F-test.