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.)RestaurantTypePrice ($)ScoreBertucci'sItalian1677Black Angus SteakhouseSeafood/Steakhouse2479Bonefish GrillSeafood/Steakhouse2685Bravo! Cucina ItalianaItalian1884Buca di BeppoItalian1781Bugaboo Creek Steak HouseSeafood/Steakhouse1877Carrabba's Italian GrillItalian2386Charlie Brown's SteakhouseSeafood/Steakhouse1775Il FornaioItalian2883Joe's Crab ShackSeafood/Steakhouse1571Johnny Carino'sItalian1781Lone Star Steakhouse & SaloonSeafood/Steakhouse1776Longhorn SteakhouseSeafood/Steakhouse1981Maggiano's Little ItalyItalian2283McGrath's Fish HouseSeafood/Steakhouse1681Olive GardenItalian1981Outback SteakhouseSeafood/Steakhouse2080Red LobsterSeafood/Steakhouse1878Romano's Macaroni GrillItalian1882The Old Spaghetti FactoryItalian1279Uno Chicago GrillItalian1676(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.)State the null and alternative hypotheses.-H0: ?1 ≥ 0Ha: ?1 < 0-H0: ?1 = 0Ha: ?1 > 0 -H0: ?1 = 0Ha: ?1 ≠ 0-H0: ?1 ≤ 0Ha: ?1 > 0Find the value of the test statistic. (Round your answer to two decimal places.)Statistic=??Find the p-value. (Round your answer to three decimal places.)p-value = ??State your conclusion.-Do not reject H0. There is insufficient evidence to conclude that there is a significant relationship.-Reject H0. There is sufficient evidence to conclude that there is a significant relationship. -Do not reject H0. There is sufficient evidence to conclude that there is a significant relationship.-Reject H0. There is insufficient evidence to conclude that there is a significant relationship. (c)Develop a dummy variable that will account for the type of restaurant (Italian or seafood/steakhouse).Let x2 = 1 if the restaurant is an Italian restaurant and x2 = 0 if the restaurant is a seafood/steakhouse.Let x2 = 1 if the restaurant is an Italian restaurant and x2 = 1 if the restaurant is a seafood/steakhouse. Let x2 = 0 if the restaurant is an Italian restaurant and x2 = 0 if the restaurant is a seafood/steakhouse. (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 = ?? (e)Is type of restaurant a significant factor in overall customer satisfaction? (Use ? = 0.05.)State the null and alternative hypotheses.-H0: ?2 ≥ 0Ha: ?2 < 0-H0: ?2 = 0Ha: ?2 ≠ 0 - H0: ?2 ≤ 0Ha: ?2 > 0-H0: ?2 = 0Ha: ?2 > 0Find the value of the test statistic. (Round your answer to two decimal places.)Statistic=??Find the p-value. (Round your answer to three decimal places.)p-value = ??State your conclusion.-Do not reject H0. There is insufficient evidence to conclude that the type of restaurant is a significant factor.-Reject H0. There is sufficient evidence to conclude that the type of restaurant is a significant factor. - Reject H0. There is insufficient evidence to conclude that the type of restaurant is a significant factor.-Do not reject H0. There is sufficient evidence to conclude that the type of restaurant is a significant factor.(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.??

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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.)

State the null and alternative hypotheses.

-H₀: ?₁ ≥ 0
H_a: ?₁ < 0

-H₀: ?₁ = 0
H_a: ?₁ > 0

-H₀: ?₁ = 0
H_a: ?₁ ≠ 0

-H₀: ?₁ ≤ 0
H_a: ?₁ > 0

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

Statistic=??

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

p-value = ??

State your conclusion.

-Do not reject H₀. There is insufficient evidence to conclude that there is a significant relationship.

-Reject H₀. There is sufficient evidence to conclude that there is a significant relationship.

-Do not reject H₀. There is sufficient evidence to conclude that there is a significant relationship.

-Reject H₀. There is insufficient evidence to conclude that there is a significant relationship.

(c)Develop a dummy variable that will account for the type of restaurant (Italian or seafood/steakhouse).

Let x₂ = 1 if the restaurant is an Italian restaurant and x₂ = 0 if the restaurant is a seafood/steakhouse.Let x₂ = 1 if the restaurant is an Italian restaurant and x₂ = 1 if the restaurant is a seafood/steakhouse. Let x₂ = 0 if the restaurant is an Italian restaurant and x₂ = 0 if the restaurant is a seafood/steakhouse.

(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 = ??

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

State the null and alternative hypotheses.

-H₀: ?₂ ≥ 0
H_a: ?₂ < 0

-H₀: ?₂ = 0
H_a: ?₂ ≠ 0

- H₀: ?₂ ≤ 0
H_a: ?₂ > 0

-H₀: ?₂ = 0
H_a: ?₂ > 0

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

Statistic=??

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

p-value = ??

State your conclusion.

-Do not reject H₀. There is insufficient evidence to conclude that the type of restaurant is a significant factor.

-Reject H₀. There is sufficient evidence to conclude that the type of restaurant is a significant factor.

- Reject H₀. There is insufficient evidence to conclude that the type of restaurant is a significant factor.

-Do not reject H₀. There is sufficient evidence to conclude that the type of restaurant is a significant factor.

(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.??

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