Question

In: Statistics and Probability

A statistical program is recommended. The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599...

A statistical program is recommended.

The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains.†Assume the following data are representative of the results reported. The variable type indicates whether the restaurant is an Italian restaurant or a seafood/steakhouse. Price indicates the average amount paid per person for dinner and drinks, minus the tip. Score reflects diners' overall satisfaction, with higher values indicating greater overall satisfaction. A score of 80 can be interpreted as very satisfied. (Let x1 represent average meal price, x2 represent type of restaurant, and y represent overall customer satisfaction.)

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 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

(a)

Develop the estimated regression equation to show how overall customer satisfaction is related to the independent variable average meal price. (Round your numerical values to two decimal places.)

ŷ =

Develop the estimated regression equation to show how overall customer satisfaction is related to the average meal price and the type of restaurant. (Use the dummy variable developed in part (c). Round your numerical values to two decimal places.)

Is type of restaurant a significant factor in overall customer satisfaction? (Use α = 0.05.)

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

(f)

Predict the Consumer Reports customer satisfaction score for a seafood/steakhouse that has an average meal price of $25. (Round your answer to two decimal places.)

How much would the predicted score have changed for an Italian restaurant? (Round your answer to two decimal places.)

The predicted satisfaction score increases by  points for Italian restaurants.

  

Solutions

Expert Solution

(a) the estimated regression equation is y=69.28+0.56*x1

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.586670267
R Square 0.344182002
Adjusted R Square 0.309665265
Standard Error 3.025748421
Observations 21
ANOVA
df SS MS F Significance F
Regression 1 91.29017857 91.29018 9.971453 0.005182
Residual 19 173.9479167 9.155154
Total 20 265.2380952
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 69.27604167 3.400463147 20.37253 2.28E-14 62.15879 76.39329
x1 0.55859375 0.17689553 3.157761 0.005182 0.188347 0.92884

(b) y=70.4431+0.5734*x1-3.0382*x2

here x2=0 for Italian and x2=1 for Seafood/Steakhouse

following regression analysis information has been generated using ms-excel and

here Italian=0 and Seafood/Steakhouse=1 as dummy variable for type(x2)

SUMMARY OUTPUT
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 69.78856 9.996691 0.001202
Residual 18 125.6609832 6.981166
Total 20 265.2380952
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 70.44306161 3.002376045 23.46244 6.02E-15 64.1353 76.75082
Price(x1) 0.573428749 0.154574333 3.709728 0.001604 0.24868 0.898177
Type(x2) -3.038207841 1.155225167 -2.62997 0.016992 -5.46525 -0.61117

(third part)

Is type of restaurant a significant factor in overall customer satisfaction? (Use α = 0.05.)

answer :yes significant as the p-value=0.017 is less than alpha=0.05

Find the value of the test statistic. (Round your answer to two decimal places.) ,

answer: test statistic t=-2.63

Find the p-value. (Round your answer to three decimal places.)

p-value =0.017

(fourth part)

(a)Predict the Consumer Reports customer satisfaction score for a seafood/steakhouse that has an average meal price of $25. (Round your answer to two decimal places.)

y^=70.4431+0.5734*x1-3.0382*x2

x1=25 and for Seafood/Steakhouse x2=1 then y^=70.4431+0.5734*x1-3.0382*1=67.40

(b)How much would the predicted score have changed for an Italian restaurant? (Round your answer to two decimal places.)

x1=25 and for Italian x2=0 then y^=70.4431+0.5734*x1-3.0382*0=70.44

(c)The predicted satisfaction score increases by  points for Italian restaurants.

answer is 70.44-67.40=3.04


Related Solutions

A statistical program is recommended. The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599...
A statistical program is recommended. The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains.†Assume the following data are representative of the results reported. The variable type indicates whether the restaurant is an Italian restaurant or a seafood/steakhouse. Price indicates the average amount paid per person for dinner and drinks, minus the tip. Score reflects diners' overall satisfaction, with higher values indicating greater overall satisfaction. A score of 80 can be interpreted as very...
DATAfile: RestaurantRatings A statistical program is recommended. The Consumer Reports Restaurant Customer Satisfaction Survey is based...
DATAfile: RestaurantRatings A statistical program is recommended. The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains.† Assume the following data are representative of the results reported. The variable type indicates whether the restaurant is an Italian restaurant or a seafood/steakhouse. Price indicates the average amount paid per person for dinner and drinks, minus the tip. Score reflects diners' overall satisfaction, with higher values indicating greater overall satisfaction. A score of 80 can be...
The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains.†...
The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains.† Assume the following data are representative of the results reported. The variable type indicates whether the restaurant is an Italian restaurant or a seafood/steakhouse. Price indicates the average amount paid per person for dinner and drinks, minus the tip. Score reflects diners' overall satisfaction, with higher values indicating greater overall satisfaction. A score of 80 can be interpreted as very satisfied. (Let x1 represent...
The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full‐service restaurant chains....
The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full‐service restaurant chains. Assume the available data on the Portal labelled Restaurant are representative of the results reported. The variable type indicates whether the restaurant is an Italian restaurant or a seafood/steakhouse. Price indicates the average amount paid per person for dinner and drinks, minus the tip. Score reflects diners’ overall satisfaction, with higher values indicating greater overall satisfaction. A score of 80 can be interpreted as...
The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains.†...
The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains.† Assume the following data are representative of the results reported. The variable type indicates whether the restaurant is an Italian restaurant or a seafood/steakhouse. Price indicates the average amount paid per person for dinner and drinks, minus the tip. Score reflects diners' overall satisfaction, with higher values indicating greater overall satisfaction. A score of 80 can be interpreted as very satisfied. (Let x1 represent...
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...
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...
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...
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...
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...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT