Statistics Tutorial 18
1. Given the data
Y
14
15
16
18
19
20
X1
5
6
6
7
8
9
X2
4
3
3
2
2
1
Based on the above data, we have given matrix and vector,
Given ( XTX ) -1 = 174.4 -16.90 -23.50
-16.9
And
(XTY) =
1.65
2.25
-23.5 2.25
3.25
102
714
243
a) Fit a multiple linear regression model to these data.
b) Find the SSE ?
c) Find the var(βj _hat) and cov(βj _hat, βk _hat) for j ,k = 0, 1, 2 and j≠k ?
d) Find the R2 and adjusted R2?
2.
a) Compute the 2-way Anova and interpret the result?
b) Is there evidence of an interaction effect? Use α = 0.05.
c) Also draw an interaction plot to see if there evidence of an interaction effect
2