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%

(a) Find the value for R² in the output and interpret it in context.
(b) Find the F-statistic and p-value in the regression ANOVA. What is the conclusion of this test?

In Data 2.12 on page 119, we introduce the dataset RestaurantTips containing information on the tipping patterns of patrons of the First Crush bistro in northern New York state. The data from 157 bills include the amount of the bill, size of the tip, percentage tip, number of customers in the group, whether or not a credit card was used, day of the week, and a coded identity of the server. The first four variables are quantitative and the last three are categorical.

Data 2.12 on page 119

The owner of a bistro called First Crush in Potsdam, New York, is interested in studying the tipping patterns of its patrons. He collected restaurant bills over a two-week period that he believes provide a good sample of his customers. The data from 157 bills are stored in RestaurantTips and include the amount of the bill, size of the tip, percentage tip, number of customers in the group, whether or not a credit card was used, day of the week, and a coded identity of the server.

Transcribed Image Text:

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