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A multiple linear regression has been performed using four independent random variables, X1, X2, X3 and X4. The regression output is:
|
|
Coefficient
|
Standard Error
|
|
Constant
|
6.96
|
|
|
X1
|
1.23
|
1.11
|
|
X2
|
5.59
|
2.35
|
|
X3
|
-2.11
|
1.96
|
|
X4
|
3.45
|
0.55
|
|
Source
|
DF
|
SS
|
MS
|
|
Regression
|
4
|
75.65
|
|
|
Error
|
|
|
|
|
Total
|
29
|
110.55
|
|
a) Complete the ANOVA table.
b) What is the multiple standard error of the estimate?
c) What is R2?
d) Write the regression equation.
e) What is the predicted value for X1=2, X2=10, X3=3 and X4=5?
f) Perform a global test of hypothesis to check if any of the regression coefficients are different from 0. What do you decide? Use the .05 significance level.
g) Do an individual test of each independent variable. Which variables would you consider eliminating? Use the .05 significance level.