STATISTICS 310 The accompanying table contains a food critic's

The accompanying table contains a food critic's ratings for food, décor,service, and cost per person for a sample of 50 restaurants located in a city and 50 restaurants located in suburban areas outside the city. You want to study differences in the cost of a meal between restaurants in the city and suburban areas and also want to be able to predict the cost of a meal. Completely analyze the data.

Test for the difference between the mean cost of a city meal and the mean cost of a suburban meal, using ? =0.05.
Choose an appropriate set of hypotheses, where ?1 is the mean cost of a meal in the city and ?2 is the mean cost of a meal in the suburbs

A. Ho: µ1 = µ2 B. Ho: µ1 > µ2

H1: µ1 < µ2 H1: µ1 = µ2

C: Ho: µ1 = µ2 D: H0: µ 1? µ 2

H1: µ1 ? µ 2 H1: µ 1 = µ 2

The test statistic is ______

The p-value is _________

Make a conclusion.

Because the p-value is less than/greater than ? =0.05, reject/do not reject. There is enough/not enough evidence to conclude that the population mean cost of a city mean is different from the population mean cost of a suburban meal.To predict the cost of a meal, construct a multiple regression model. Let X1=food rating, X2 equals=decor rating, X3 =service rating, and X4=location. Determine the VIF for each independent variable.

VIF for X1=

VIF for X2=

VIF for X3=

VIF for X4=

Which variable or variables, if any, should be eliminated due to multicollinearity? Note that if any variables are eliminated due to the VIFs calculated above, recalculate the VIFs for the remaining variables and continue this process (removing variables and recalculating VIFs) until no variables need to be eliminated due to multicollinearity. Select all that apply.

A. X3

B. X1

C. X2

D. X4

E. No variables should be eliminated

Perform a best-subsets regression. Use the results to generate a list of models in which all variables are significant (using ?=0.05) and that satisfies the Cp statistic criterion. Of these models, select the model that has the highest adjusted r2.
Select the correct model below and fill in the answer boxes to complete your choice.

A. Yi = ___ + ____X1i +_____X2i + _____ X3i + _____X4i

B. Yi = _____ + ____ X1i + ______X2i + ______X3i

C. Yi = _____ + _____X1i+_______X3i

D. Yi= _______ + _____X1i + ______X3i + ______X4i

Use the regression to address the difference between the costs of city and suburban meals. Choose the correct answer below.

A. Taking the ratings into account, low-service suburban meals are significantly more expensive than high-service suburban meals

B. Taking the ratings into account, suburban meals are significantly more expensive than city meals, on average.

C. Taking the ratings into account, city meals are significantly more expensive than suburban meals, on average..

D. Taking the ratings into account, there is not a significant difference between the mean costs of city and suburban meals.

Food_Rating Decor_Rating Service_Rating
30
22
31
15
20
25
23
19
21
19
18
18
24
16
18
22
22
21
22
20
20
20
19
19
21
17
19
20
18
18
23
22
24
20
19
20
21
19
21
24
19
21
25
23
23
22
21
21
23
15
22
26
22
24
21
23
21
24
15
19
21
15
19
23
16
16
25
21
26
22
20
21
26
25
24
23
21
21
22
19
17
26
20
23
26
23
25
24
23
24
22
23
23
24
16
23
20
17
19
25
19
23
23
20
21
21
19
22
20
16
18
23
15
18
26
24
24
21
18
18
22
16
19
19
23
21
24
19
21
23
16
20
24
26
22

Location_(0=City_1=Suburbs)

Cost
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

40
30
43
32
44
44
50
42
44
36
61
50
51
50
76
53
44
77
57
43
29
34
77
50
74
56
67
57
66
80
68
42
48
60
35
45
32
25
74
43
39
55
65
35
61

21
21
23
23
23
24
22
18
22
22
23
20
19
22
27
19
22
24
19
21
21
23
23
21
24
20
24
23
23
23
19
22
26
22
19
21
26
22
21
20
22
23
24
23
24
26

17
17
19
19
14
20
18
13
23
18
25
12
18
19
21
14
11
22
15
23
19
19
20
13
19
18
22
17
16
18
12
17
27
21
15
12
18
25
21
20
18
20
21
27
24
17

18
19
22
21
19
22
22
18
20
24
24
18
19
21
27
18
19
24
19
21
21
23
22
19
22
20
24
22
21
22
22
21
24
23
17
20
22
21
21
20
22
19
23
22
22
24

0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

37
54
41
33
27
47
48
35
59
44
51
37
36
43
52
34
38
51
34
51
34
51
56
26
34
34
44
40
31
54
41
50
71
60
37
27
34
48
39
44
41
37
47
67
68
49

22
24
20
26
22
18
26
25
22

22
18
19
19
15
20
27
26
25

19
22
20
23
21
18
25
23
22

1
1
1
1
1
1
1
1
1

29
33
39
39
28
46
70
60
52