Question

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

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.)

ŷ =

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.

Answer 1

Considering Italian restaurant as 1 and Seafood/Steakhouse as 0.

The regression results are

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
Intercept	67.40485	3.053452	22.07497	1.74E-14
Type	3.038208	1.155225	2.62997	0.016992
Price ($)	0.573429	0.154574	3.709728	0.001604

Y = 67.40 + 3.04*Type + 0.57*Price

Y =67.40+ 0.57X₁ + 3.04X₂

p-value for overall regression = 0.001

f) Predict the Consumer Reports customer satisfaction score for a seafood/steakhouse that has an average meal price of $25

Y = 67.40 + 0.57*25 + 3.04*0 = 81.65

Predict the Consumer Reports customer satisfaction score for a Italian that has an average meal price of $25

Y = 67.40 + 0.57*25 + 3.04*1 = 84.69

The predicted satisfaction score increases by 3.04 points for Italian restaurants.