Question: A past graduate of Eco 221 is attempting to make sense of the relationship between groups of persons eating at restaurants and the tip the group leaves for the waitstaff. The proud graduate remembered to compute the descriptive statistics and male scatter diagrams of the data before attempting further analysis. He has 244 observations (244 groups who ate at this restaurant) on the following variables

TIP tip in dollars

TOTBILL total bill including tax, in dollars

SEX the sex of the person paying the bill (1 = female, 0 = male)

SMOKER whether or not there is a smoker in the group ( 1 = yes, 0 = no)

DAY day of the week (3 = Thursday, 4 = Friday, 5= Saturday, 6 = Sunday)

TIME 0 = day, 1 = night

SIZE number of people in the group

After due deliberation, our graduate has decided on the following model:

TIP = b₀ + b₁ TOTBILL + b₂ SIZE + b₃ SEX + e

She then estimated the model using Ordinary Least Squares and got the output below:.

Regression Analysis: TIP versus TOTBILL, SIZE, SEX

The regression equation is

TIP = 0.655 + 0.0929 TOTBILL + 0.193 SIZE + 0.026 SEX

Predictor Coef SE Coef T P

Constant 0.6555 0.2063 3.18 0.002

TOTBILL 0.09292 0.009196 10.10 0.000

SIZE 0.19259 0.08549 2.25 0.025

SEX 0.0264 0.1372 0.19 0.847

S = 1.01554 R-Sq = 46.8% R-Sq(adj) = 46.1%

Analysis of Variance

Source DF SS MS F P

Regression 3 217.697 72.566 70.36 0.000

Residual Error 240 247.516 1.031

Total 243 465.212

(a) What is the effect on the waitperson’s tip of adding one person to the group?

(b) Explain whether the sex of the person paying the bill is an important variable in estimating the tip.

(c) What would the predicted tip be if there were 5 people in the group, a woman paid the bill and the total bill came to $150?

d) Given the limits on the data, explain how you feel the model could be improved (or why it can’t be improved if you believe this is the best possible model).