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 RSQ (R-squared) value? (Note: This is regular R^2, NOT Adjusted R^2).

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

Answer:

a) regression equation : Score = 70.4431 +0.5734*Price - 3.0382*type_dummy

b) RSQ (R-squared) value=0.5262

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Solution:

• Part a.

  Regression analysis using MS-EXCEL gives following results.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.725419
R Square	0.526233
Adjusted R Square	0.473593
Standard Error	2.64219
Observations	21
ANOVA
	df	SS	MS	F	Significance F
Regression	2	139.5771	69.78856	9.996691	0.001202
Residual	18	125.661	6.981166
Total	20	265.2381
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	70.44306	3.002376	23.46244	6.02E-15	64.1353	76.75082	64.1353	76.75082
type_dummy	-3.03821	1.155225	-2.62997	0.016992	-5.46525	-0.61117	-5.46525	-0.61117
Price ($)	0.573429	0.154574	3.709728	0.001604	0.24868	0.898177	0.24868	0.898177

• Using This we get the regression equation as,

  Score = 70.4431 +0.5734*Price - 3.0382*type_dummy

• b) RSQ (R-squared) value=0.5262

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If you have any doubt please let me know through comment
Please give positive vote if you find this solution helpful. Thank you!

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Input Data

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