Question

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 = ___________

(b)

At the 0.05 level of significance, test whether the estimated regression equation developed in part (a) indicates a significant relationship between overall customer satisfaction and average meal price. (Use an F test.)

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 = 0.005

(d)

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.) __________9.99 and 10.00 are both wrong

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

p-value = ____________0.001 and 0.00 are both wrong

Predict the Consumer Reports customer satisfaction score for a seafood/steakhouse that has an average meal price of $15. (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.) 75.95

The predicted satisfaction score increases by __________ points for Italian restaurants

Answer 1

a) Using excel we get below regression output:

Regression Statistics
Multiple R	0.58667
R Square	0.344182
Adjusted R Square	0.309665
Standard Error	3.025748
Observations	21
ANOVA
	df	SS	MS	F	Significance F
Regression	1	91.29018	91.29018	9.971453	0.005182
Residual	19	173.9479	9.155154
Total	20	265.2381
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	69.27604	3.400463	20.37253	2.28E-14	62.15879	76.39329
Price ($)	0.558594	0.176896	3.157761	0.005182	0.188347	0.92884

So,

y = 69.27 + 0.558x₁

b) From above output, Significance F = 0.005

This is less than 0.05 significance level. Hence, there is a significant relationship between overall customer satisfaction and average meal price.

p value: 0.005

Q. c) not provide

d) Dummy variable for restaurant type:

Seafood/Steakhouse	0
Italian	1

Now regression 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%
Intercept	67.40485	3.053452	22.07497	1.74E-14	60.98979	73.81992
Type	3.038208	1.155225	2.62997	0.016992	0.61117	5.465246
Price ($)	0.573429	0.154574	3.709728	0.001604	0.24868	0.898177

So,

y = 67.41 + 3.04x₂ + 0.57x₁

Significance F = 0.001

Both p values are in above table underlined.

Last part:

For average meal price of $15 at seafood/steakhouse

y = 67.41 + 3.04x₂ + 0.57x₁

₌ 67.41 + 3.04*0 + 0.57*15

=75.96

For average meal price of $15 at italian

=67.41 + 3.04*1 + 0.57*15

=79

So,

The predicted satisfaction score increases by 3.04 points for Italian restaurants