Question

In: Statistics and Probability

The Consumer Reports customer satisfaction survey is based upon 148,599 visits to full service restaurant chains....

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. Which restaurant comes "closest" to being an "outlier" in a statistical sense based upon the regression model above?

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

Solutions

Expert Solution

Result:

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. Which restaurant comes "closest" to being an "outlier" in a statistical sense based upon the regression model above?

The estimated regression line is

Score = 67.405+0.573*price+3.038*type

Both variables price and type are significantly prediction the score. 52.6% variance in score is explained by the model.

The Studentized residual for Restaurant Joe's Crab Shack is -2.061. This restaurant comes closest" to being an outlier.

Excel Addon Megastat used.

Menu used: correlation/Regression ---- Regression Analysis.

Regression Analysis

R²

0.526

Adjusted R²

0.474

n

21

R

0.725

k

2

Std. Error of Estimate

2.642

Dep. Var.

Score

Regression output

confidence interval

variables

coefficients

std. error

   t (df=18)

p-value

95% lower

95% upper

Intercept

a =

67.405

3.053

22.075

1.74E-14

60.990

73.820

Price ($)

b1 =

0.573

0.155

3.710

.0016

0.249

0.898

Type

b2 =

3.038

1.155

2.630

.0170

0.611

5.465

ANOVA table

Source

SS

df

MS

F

p-value

Regression

139.577

2  

69.789

10.00

.0012

Residual

125.661

18  

6.981

Total

265.238

20  

Studentized

Studentized

Deleted

Observation

Score

Predicted

Total =

Residual

+ Regression

Leverage

Residual

Residual

Cook's D

1

77.0

79.6

-2.8

-2.6

-0.2

0.116

-1.054

-1.057

0.049

2

79.0

81.2

-0.8

-2.2

1.4

0.186

-0.909

-0.904

0.063

3

85.0

82.3

5.2

2.7

2.5

0.268

1.188

1.203

0.172

4

84.0

80.8

4.2

3.2

1.0

0.093

1.285

1.311

0.056

5

81.0

80.2

1.2

0.8

0.4

0.101

0.323

0.315

0.004

6

77.0

77.7

-2.8

-0.7

-2.1

0.103

-0.290

-0.283

0.003

7

86.0

83.6

6.2

2.4

3.8

0.153

0.974

0.973

0.057

8

75.0

77.2

-4.8

-2.2

-2.7

0.114

-0.866

-0.859

0.032

9

83.0

86.5

3.2

-3.5

6.7

0.385

-1.689

-1.789

0.596

10

71.0

76.0

-8.8

-5.0

-3.8

0.155

-2.061

-2.291

0.259

11

81.0

80.2

1.2

0.8

0.4

0.101

0.323

0.315

0.004

12

76.0

77.2

-3.8

-1.2

-2.7

0.114

-0.464

-0.453

0.009

13

81.0

78.3

1.2

2.7

-1.5

0.100

1.077

1.082

0.043

14

83.0

83.1

3.2

-0.1

3.2

0.128
orchestra answered 1 year ago
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