Question

A study of emergency service facilities investigated the relationship between the number of facilities and the average distance traveled to provide the emergency service. The following table gives the data collected.

Number of Facilities	Average Distance (miles)
9	1.65
11	1.12
16	0.82
21	0.62
27	0.51
30	0.47

(a)Develop an estimated regression equation for the data corresponding to a second-order model with one predictor variable. (Round your numerical values to four decimal places.)

ŷ = ____

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)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 = ______

(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 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.)_____

(f)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.)

The predicted satisfaction score increases by____ points for Italian restaurants.

Answer 1

$\widehat{y} = \boldsymbol{(0.0035)} \ x^2 -\boldsymbol{(0.1844)}\ x +\boldsymbol{2.8916}$

In Excel

Insert > plot > more > option > polynomial > select equation on graph