In Exercise D.9, we use the size of the bill to predict the tip. In this exercise, we use both the size of the bill and the number of guests to predict the size of the tip. Some regression output is shown for this analysis:

The regression equation is

Tip = ˆ’ 0.252 + 0.184 Bill ˆ’ 0.036 Guests

(a) What is the regression equation? What tip is predicted for three guests with a $30 bill?
(b) There are two explanatory variables in the model. Interpret the coefficient of each.
(c) Give the p-value for testing the slope of each explanatory variable, and indicate whether each is significant in the model.
(d) Give the value of R² and interpret it in context.
(e) Find the F-statistic and p-value in the regression ANOVA. What are the hypotheses and conclusion of this test?

Exercise D.9

We have seen in earlier exercises that the conditions are met for using a regression line to predict the Tip from the size of the Bill. Some regression output is shown for fitting this linear model:

The regression equation is

Tip = - 0.292 + 0.182 Bill

S = 0.979523 R-Sq = 83.7% R-Sq(adj) = 83.6%

Transcribed Image Text:

Coef Predictor SE Coef т Constant -0.2524 0.2019 -1.25 0.213 Bill 0.183751 0.007815 23.51 0.000 Guests -0.0357 0.1019 -0.35 0.727 S = 0.982307 R-Sq = 83.7% R-Sq(adj) = 83.5% Analysis of Variance Source DF MS Regression 2 765.65 382.82 396.74 0.000 0.96 Residual Error 154 148.60 Total 156 914.25 Analysis of Variance Source Regression Residual Error Total DF 765.53 148.72 914.25 MS 765.53 0.96 797.87 0.000 155 156