Question: I need help answering these questions. I keep getting incorrect answers. A company publishes restaurant ratings for various locations. The accompanying data table contains the
I need help answering these questions. I keep getting 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 61 City
68 65 City
50 20 City
74 77 City
52 33 City
48 38 City
64 45 City
55 43 City
56 40 City
48 41 City
65 47 City
55 31 City
66 57 City
57 57 City
53 33 City
69 58 City
51 23 City
49 39 City
61 46 City
51 46 City
62 43 City
58 33 City
67 60 City
53 43 City
57 50 City
61 30 City
51 32 City
68 78 City
54 43 City
42 24 City
57 40 City
62 51 City
55 47 City
64 55 City
68 67 City
57 46 City
49 42 City
63 32 City
67 53 City
50 29 City
60 42 City
65 58 City
61 71 City
68 61 City
54 63 City
60 61 City
54 47 City
73 77 City
58 66 City
54 40 City
60 53 Suburban
61 47 Suburban
50 42 Suburban
57 45 Suburban
63 44 Suburban
51 32 Suburban
65 40 Suburban
59 32 Suburban
56 34 Suburban
52 36 Suburban
61 56 Suburban
59 31 Suburban
58 52 Suburban
52 43 Suburban
51 36 Suburban
64 56 Suburban
56 50 Suburban
52 35 Suburban
59 30 Suburban
66 41 Suburban
57 40 Suburban
62 37 Suburban
70 54 Suburban
65 41 Suburban
50 33 Suburban
55 44 Suburban
56 38 Suburban
53 45 Suburban
69 39 Suburban
64 44 Suburban
56 38 Suburban
65 57 Suburban
75 61 Suburban
60 47 Suburban
49 30 Suburban
60 35 Suburban
66 69 Suburban
64 37 Suburban
60 51 Suburban
59 35 Suburban
55 26 Suburban
56 46 Suburban
57 24 Suburban
57 41 Suburban
48 34 Suburban
70 62 Suburban
64 36 Suburban
46 25 Suburban
64 55 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 (16.159 OR 1.247 OR 25.264 OR 5.899) 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 (less OR greater) than the value of , (reject OR do not 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 , (do not reject OR reject)
the null hypothesis. The second independentvariable, Location, (does not appear OR appears) 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 (Summated Rating OR Location OR Cost) by to dollars.
(Round to three decimal places as needed. Use ascendingorder.)
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