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

(a) Which variable might we try eliminating first to possibly improve this model?
(b) What is R² for this model? Do we expect R² to increase, decrease, or remain the same if we eliminate the variable chosen in part (a)? What type of change in R² would indicate that removing the variable chosen in part (a) was a good idea? A bad idea?
(c) What is the p-value for ANOVA for the original3-predictor model? Is the p-value most likely to increase, decrease, or remain the same if we eliminate the variable chosen in part (a)? What type of change in the p-value for ANOVA would indicate that removing the variable chosen in part (a) was a good idea? A bad idea?
(d) What is the F-statistic from ANOVA for this model? Is this F-statistic most likely to increase, decrease, or remain the same if we eliminate an insignificant variable? What type of change in the F-statistic would indicate that removing the variable chosen in part (a) was a good idea?

Use the given output to answer questions about how a model might change.

The regression equation is Y = 15.1 + 0.135 X1 - 0.696 X2 + 0.025 X3 Predictor Coef SE Coef Constant 15.069 5.821 2.59 0.020 0.1353 X1 0.2354 0.57 0.573 X2 -0.6962 0.3029 -2.30 0.035 X 0.0253 0.1920 0.13 0.897 S= 4.92431 R-Sq = 41.7% R-Sq(adj) = 30.7% Analysis of Variance Source DF MS 0.031 Regression Residual Error 3 277.02 92.34 3.81 16 387.98 24.25 665.00 Total 19