Question

The Consumer Reports customer satisfaction survey is based upon 148,599 visits to full service restaurant chains. Assume this data set is representative of the results reported. The variable restaurant “type” indicates whether the restaurant is an Italian restaurant or a seafood/steakhouse. Price indicates the average amount a person paid for dinner and drinks minus the tip. Score reflects overall customer satisfaction and a score of 80 can be interpreted as very satisfied. Assume alpha = 0.05 for all parts of this question.

First, develop a dummy variable to indicate the restaurant’s “type”. Use a dummy variable code of ‘0’ to indicate an Italian restaurant and a ‘1’ to indicate a seafood/steakhouse. Develop a regression equation predicting the customer satisfaction score based upon both price and restaurant type.  

What is the predicted satisfaction score for an Italian restaurant when average meal price spent is $20?

Restaurant	Type	Price ($)	Score
Bertucci's	Italian	16	77
Black Angus Steakhouse	Seafood/Steakhouse	24	79
Bonefish Grill	Seafood/Steakhouse	26	85
Bravo! Cucina Italiana	Italian	18	84
Buca di Beppo	Italian	17	81
Bugaboo Creek Steak House	Seafood/Steakhouse	18	77
Carrabba's Italian Grill	Italian	23	86
Charlie Brown's Steakhouse	Seafood/Steakhouse	17	75
Il Fornaio	Italian	28	83
Joe's Crab Shack	Seafood/Steakhouse	15	71
Johnny Carino's Italian	Italian	17	81
Lone Star Steakhouse & Saloon	Seafood/Steakhouse	17	76
LongHorn Steakhouse	Seafood/Steakhouse	19	81
Maggiano's Little Italy	Italian	22	83
McGrath's Fish House	Seafood/Steakhouse	16	81
Olive Garden	Italian	19	81
Outback Steakhouse	Seafood/Steakhouse	20	80
Red Lobster	Seafood/Steakhouse	18	78
Romano's Macaroni Grill	Italian	18	82
The Old Spaghetti Factory	Italian	12	79
Uno Chicago Grill	Italian	16	76

Answer 1

after creating the dummy variable we have the data

Restaurant	Type	Price ($)	Score
Bertucci's	0	16	77
Black Angus Steakhouse	1	24	79
Bonefish Grill	1	26	85
Bravo! Cucina Italiana	0	18	84
Buca di Beppo	0	17	81
Bugaboo Creek Steak House	1	18	77
Carrabba's Italian Grill	0	23	86
Charlie Brown's Steakhouse	1	17	75
Il Fornaio	0	28	83
Joe's Crab Shack	1	15	71
Johnny Carino's Italian	0	17	81
Lone Star Steakhouse & Saloon	1	17	76
LongHorn Steakhouse	1	19	81
Maggiano's Little Italy	0	22	83
McGrath's Fish House	1	16	81
Olive Garden	0	19	81
Outback Steakhouse	1	20	80
Red Lobster	1	18	78
Romano's Macaroni Grill	0	18	82
The Old Spaghetti Factory	0	12	79
Uno Chicago Grill	0	16	76

uisng excel>data>data analysis>Regression

we have

Regression Analysis
Regression Statistics
Multiple R	0.72541938
R Square	0.526233277
Adjusted R Square	0.47359253
Standard Error	2.642189572
Observations	21
ANOVA
	df	SS	MS	F	Significance F
Regression	2	139.577112	69.78855602	9.996690909	0.001202489
Residual	18	125.6609832	6.981165733
Total	20	265.2380952
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	70.44306161	3.002376045	23.46243793	6.01906E-15	64.1353036	76.75081961
Type	-3.038207841	1.155225167	-2.629970268	0.016992448	-5.465245855	-0.611169827
Price ($)	0.573428749	0.154574333	3.709728122	0.001603536	0.248680127	0.898177372

a regression equation predicting the customer satisfaction score based upon both price and restaurant type is

y= 70.443 -3.038 *Type+0.573 *Price

the predicted satisfaction score for an Italian restaurant when the age meal price spent is $20 is

y= 70.443 -3.038 *0+0.573 *20=81.903