Question
I need help answering these questions. I get incorrect answers A company publishes restaurant ratings for various locations. The accompanying data table contains the summated
I need help answering these questions. I get incorrect answers
A company publishes restaurant ratings for various locations. The accompanying data table contains the summated rating forfood, dcor,service, and cost per person for a sample of 50 restaurants located in a city and 50 restaurants located in a suburb. Develop a regression model to predict the cost perperson, based on the summated rating variable and a dummy variable concerning location(city vs.suburban).
Complete parts(a) through(f). For(a) through(d), do not include an interaction term.
Summated_Rating Cost_($) Location
60 65 City
68 67 City
50 26 City
74 80 City
52 34 City
48 39 City
64 45 City
55 41 City
56 39 City
48 46 City
65 43 City
55 29 City
66 57 City
57 58 City
53 31 City
69 57 City
51 25 City
49 40 City
61 43 City
51 44 City
62 39 City
58 32 City
67 55 City
53 44 City
57 47 City
61 25 City
51 35 City
68 79 City
54 44 City
42 19 City
57 39 City
62 48 City
55 46 City
64 51 City
68 61 City
57 50 City
49 38 City
63 31 City
67 51 City
50 27 City
60 46 City
65 59 City
61 66 City
68 57 City
54 64 City
60 61 City
54 46 City
73 76 City
58 64 City
54 44 City
60 53 Suburban
61 43 Suburban
50 39 Suburban
57 40 Suburban
63 44 Suburban
51 27 Suburban
65 38 Suburban
59 37 Suburban
56 32 Suburban
52 39 Suburban
61 53 Suburban
59 28 Suburban
58 50 Suburban
52 43 Suburban
51 33 Suburban
64 53 Suburban
56 48 Suburban
52 36 Suburban
59 27 Suburban
66 43 Suburban
57 40 Suburban
62 38 Suburban
70 53 Suburban
65 43 Suburban
50 31 Suburban
55 44 Suburban
56 42 Suburban
53 46 Suburban
69 39 Suburban
64 42 Suburban
56 36 Suburban
65 56 Suburban
75 62 Suburban
60 47 Suburban
49 30 Suburban
60 37 Suburban
66 71 Suburban
64 37 Suburban
60 48 Suburban
59 34 Suburban
55 28 Suburban
56 45 Suburban
57 26 Suburban
57 42 Suburban
48 35 Suburban
70 63 Suburban
64 35 Suburban
46 23 Suburban
64 53 Suburban
64 60 Suburban
a. State the multiple regression equation that predicts the cost per person, based on the summatedrating, X1, and thelocation, X2. Define X2 to be 0 for restaurants located in a city and let X2 be 1 for restaurants located in a suburb.
Yi= ( )+( )X1i+( )X2i
(Round to three decimal places asneeded.)
b. Interpret the regression coefficients in(a).
Holding constant whether a restaurant is in a city or asuburb, for each increase of 1 unit in the summatedrating, the predicted cost per person is estimated to change by dollars. Holding constant the summatedrating, the presence of the restaurant in a (city OR suburb) is estimated to decrease the predicted cost per person by (1.219 OR 24.247 OR 10.014 OR 5.805) dollars over the cost per person of a restaurant in a (suburb OR city)
(Round to three decimal places asneeded.)
c. At the 0.05 level ofsignificance, determine whether each independent variable makes a contribution to the regression model.
Test the first independentvariable, SummatedRating. Determine the null and alternative hypotheses.
H0: 1
H1: 1
The test statistic for the first independentvariable, SummatedRating, is
tSTAT=
(Round to three decimal places asneeded.)
Thep-value for the first independentvariable, SummatedRating, is
(Round to four decimal places asneeded.)
Since thep-value is (greater OR less) than the value of , (do not reject OR reject) the null hypothesis. The first independentvariable, SummatedRating, (appears OR does not appear) to make a contribution to the regression model.
Test the second independentvariable, Location. Determine the null and alternative hypotheses.
H0: 2
H1: 2
The test statistic for the second independentvariable, Location, is
tSTAT=
(Round to three decimal places asneeded.)
Thep-value for the second independentvariable, Location, is
(Round to four decimal places asneeded.)
Since thep-value is (greater OR less) than the value of , (reject OR do not reject) the null hypothesis. The second independentvariable, Location, (appears OR does not appear) to make a contribution to the regression model.
d. Construct and interpret a95% confidence interval estimate of the population slope of the relationship between Cost and SummatedRating.
Taking into account the effect of (Summated Rating OR Cost OR Location) the estimated effect of a1-unit increase in SummatedRating is to change the (Location OR Cost OR summated Rating) by to dollars.
(Round to three decimal places as needed. Use ascendingorder.)
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