A magazine publishes restaurant ratings for various locations around the world. The magazine rates the restaurants for food,

decor,

service, and the cost per person. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the three ratings. The magazine has compiled the accompanying table of this summated ratings variable and the cost per person for 25 restaurants in a major city. Complete parts (a) through (e) below.

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Part 1

a. Construct a scatter plot. Choose the correct graph below.

A.

090090RatingCost($)

A scatter plot has a horizontal axis labeled Rating from 0 to 90 in increments of 10 and a vertical axis labeled Cost ($) from 0 to 90 in increments of 10. A series of plotted points fall exactly on a line that rises from left to right, where the points range from (45,45) to (75,75). All coordinates are approximate.

B.

090090RatingCost($)

A scatter plot has a horizontal axis labeled Rating from 0 to 90 in increments of 10 and a vertical axis labeled Cost ($) from 0 to 90 in increments of 10. A series of plotted points are clustered around a line that rises from left to right passing through the points (50,34) and (60,47). All coordinates are approximate

C.

090090RatingCost($)

A scatter plot has a horizontal axis labeled Rating from 0 to 90 in increments of 10 and a vertical axis labeled Cost ($) from 0 to 90 in increments of 10. A series of plotted points fall exactly on a line that rises from left to right, where the points range from (26,26) to (88,88). All coordinates are approximate.

D.

090090RatingCost($)

A scatter plot has a horizontal axis labeled Rating from 0 to 90 in increments of 10 and a vertical axis labeled Cost ($) from 0 to 90 in increments of 10. A series of plotted points are clustered around a line that rises from left to right passing through the points (30,52) and (50,61). All coordinates are approximate.

Part 2

b. Assuming a linear relationship, use the least-squares method to compute the regression coefficients

b0

and

b1.

b0=enter your response here

and

b1=enter your response here

(Round to two decimal places as needed.)

Part 3

c. Interpret the meaning of the Y-intercept,

b0,

and the slope,

b1.

Choose the correct answer below.

A.

The Y-intercept,

b0,

implies that if the summated rating of a restaurant is zero, the cost per meal is equal to

b0,

in dollars. The slope,

b1,

implies that for each increase of 1 in the summated rating, the cost per person is expected to decrease by

b1,

in dollars.

B.

A practical interpretation of the Y-intercept

b0

is not meaningful because no operating restaurant is likely to have a rating of zero. The slope

b1

implies that for each increase of 1 in the summated rating, the cost per person is expected to increase by the value of

b1,

in dollars.

C.

The Y-intercept,

b0,

implies that if the summated rating of a restaurant is zero, the cost per person is

b0,

in dollars. The slope,

b1,

implies the average cost per person is

b1

dollars.

D.

The Y-intercept,

b0,

implies that if the summated rating of a restaurant is zero, the cost per meal is equal to

b0,

in dollars. The slope,

b1,

implies that for each increase of 1dollar in the cost per person, the summated rating is expected to increase by

b1.

Part 4

d. Predict the mean cost per person for a restaurant with a summated rating of

60.

Yi=$enter your response here

per person (Round to the nearest cent as needed.)

Part 5

e. What should you tell the owner of a group of restaurants in this geographical area about the relationship between the summated rating and the cost of a meal?

A.

As expected, the higher the summated rating of the restaurant, the higher the restaurant can charge per meal.

B.

As expected, the summated rating of the restaurant is not associated with what the restaurant can charge per meal.

C.

As expected, the higher the summated rating of the restaurant, the less the restaurant can charge per meal.

D.

As expected, the lower the summated rating of the restaurant, the higher the restaurant can charge per meal.

Next

Summated_Rating Cost_($_per_person) 54 37 66 52 69 62 68 61 63 44 57 42 52 46 65 42 50 31 50 35 52 42 49 35 73 88 62 52 56 37 50 35 58 31 45 26 54 39 58 46 63 65 66 60 51 29 75 45 67 47