Question

# Use the multiple regression output shown to answer the following questions. The regression equation is Y=9.40+0.332X⁢1+0.067X⁢2-0.251X⁢3...

Use the multiple regression output shown to answer the following questions.

 The regression equation is Y=9.40+0.332X⁢1+0.067X⁢2-0.251X⁢3

Coef SE Coef T P Predictor 9.395 6.858 1.37 0.184 0.3316 0.8962 0.37 0.716 0.0666 -0.0520 -1.28 0.214 -0.2508 -0.1036 2.42 0.025
Source DF SS MS F P Analysis of Variance Regression 3 86.8 28.93 1.23 0.322 Residual Error 21 493.5 23.5 Total 24 580.3

a) Which variable might we try eliminating first to possibly improve this model?

b) What is R2 for this model?
c) Do we expect R2 to increase, decrease, or remain the same if we eliminate the variable chosen in part (a)?

c) What is the p-value for ANOVA for the original 3-predictor model?
d) What is the F-statistic from ANOVA for this model?

Solution:

a) Which variable might we try eliminating first to possibly improve this model?

Answer: X1 because it has the largest p-value among the independent variables.

b) What is R2 for this model?

c) Do we expect R2 to increase, decrease, or remain the same if we eliminate the variable chosen in part (a)?
Answer: We would expect R2 to increase because we are eliminating the most insignificant variable from the model

c) What is the p-value for ANOVA for the original 3-predictor model?

d) What is the F-statistic from ANOVA for this model?