Question

Zagat’s publishes restaurant ratings for various locations in the United States. The file Restaurants contains the Zagat rating for food, décor, service, and the cost per person for a sample of 100 restaurants located in New York City and in a suburb of New York City. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the ratings for food, décor, and service.

a. Construct a scatter plot.

b. Assuming a linear relationship, use the least-squares method to compute the regression coefficients b0 and b1.

c. Interpret the meaning of the Y-intercept, b0, and the slope, b1, in this problem.

d. Predict the mean cost per person for a restaurant with a summated rating of 50.

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?

Location	Food	Décor	Service	Summated Rating	Coded Location	Cost
City	22	14	19	55	0	33
City	20	15	20	55	0	26
City	23	19	21	63	0	43
City	19	18	18	55	0	32
City	24	16	18	58	0	44
City	22	22	21	65	0	44
City	22	20	20	62	0	50
City	20	19	19	58	0	42
City	21	17	19	57	0	44
City	20	18	18	56	0	36
City	23	22	24	69	0	61
City	20	19	20	59	0	50
City	21	19	21	61	0	51
City	24	19	21	64	0	50
City	25	23	23	71	0	76
City	22	21	21	64	0	53
City	23	15	22	60	0	44
City	26	22	24	72	0	77
City	21	23	21	65	0	57
City	24	15	19	58	0	43
City	21	15	19	55	0	29
City	23	16	16	55	0	34
City	25	21	26	72	0	77
City	22	20	21	63	0	50
City	26	25	24	75	0	74
City	23	21	21	65	0	56
City	22	19	17	58	0	67
City	26	20	23	69	0	57
City	26	23	25	74	0	66
City	24	23	24	71	0	80
City	22	23	23	68	0	68
City	24	16	23	63	0	42
City	20	17	19	56	0	48
City	25	19	23	67	0	60
City	23	20	21	64	0	35
City	21	19	22	62	0	45
City	20	16	18	54	0	32
City	23	15	18	56	0	25
City	26	24	24	74	0	74
City	21	18	18	57	0	43
City	22	16	19	57	0	39
City	19	23	21	63	0	55
City	24	19	21	64	0	65
City	23	16	20	59	0	35
City	24	26	22	72	0	61
City	21	17	18	56	0	37
City	21	17	19	57	0	54
City	23	19	22	64	0	41
City	23	19	21	63	0	33
City	23	14	19	56	0	27
Suburban	24	20	22	66	1	47
Suburban	22	18	22	62	1	48
Suburban	18	13	18	49	1	35
Suburban	22	23	20	65	1	59
Suburban	22	18	24	64	1	44
Suburban	23	25	24	72	1	51
Suburban	20	12	18	50	1	37
Suburban	19	18	19	56	1	36
Suburban	22	19	21	62	1	43
Suburban	27	21	27	75	1	52
Suburban	19	14	18	51	1	34
Suburban	22	11	19	52	1	38
Suburban	24	22	24	70	1	51
Suburban	19	15	19	53	1	34
Suburban	21	23	21	65	1	51
Suburban	21	19	21	61	1	34
Suburban	23	19	23	65	1	51
Suburban	23	20	22	65	1	56
Suburban	21	13	19	53	1	26
Suburban	24	19	22	65	1	34
Suburban	20	18	20	58	1	34
Suburban	24	22	24	70	1	44
Suburban	23	17	22	62	1	40
Suburban	23	16	21	60	1	31
Suburban	23	18	22	63	1	54
Suburban	19	12	22	53	1	41
Suburban	22	17	21	60	1	50
Suburban	26	27	24	77	1	71
Suburban	22	21	23	66	1	60
Suburban	19	15	17	51	1	37
Suburban	21	12	20	53	1	27
Suburban	26	18	22	66	1	34
Suburban	22	25	21	68	1	48
Suburban	21	21	21	63	1	39
Suburban	20	20	20	60	1	44
Suburban	22	18	22	62	1	41
Suburban	23	20	19	62	1	37
Suburban	24	21	23	68	1	47
Suburban	23	27	22	72	1	67
Suburban	24	24	22	70	1	68
Suburban	26	17	24	67	1	49
Suburban	22	22	19	63	1	29
Suburban	24	18	22	64	1	33
Suburban	20	19	20	59	1	39
Suburban	26	19	23	68	1	39
Suburban	22	15	21	58	1	28
Suburban	18	20	18	56	1	46
Suburban	26	27	25	78	1	70
Suburban	25	26	23	74	1	60
Suburban	22	25	22	69	1	52

Answer 1

a). the scatter plot is given below:

After performing regression in MINITAB, results are given below:

b). b0=-46.77 and b1=1.496.

c). even there is no food decor and service ratings, the cost is -46.77 which is negative.

one unit increase in food decor and service ratings will cause 1.496 times increase in cost.

d). cost =-46.77+1.496(50) = 28.03

e)since the p-value is 0.000, the model is significant.