3) 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] = ₀ + ₁x₁ + ₂x₂ + ₃x_3. Suppose you want to test

H₀ : ₃ = 0. Please carry out an F- test.

C) For the model

E[y|x] = ₀ + ₁x₁ + ₂x₂ + ₃x_3, suppose you want to test

H₀ : ₁ = ₃ = 0. In order to carry out an F-test for that, what

is the other regression ANOVA table we need.