Freshcrim specializes in the sales of ice cream from street trolleys in the centers of many cities. Some factors that may determine the sales of ice cream are: the atmospheric temperature, the location of the trolley, the rain and the humidity. However, there exists a hypothesis that the sales of ice cream during the summer are significantly correlated only with atmospheric temperature. They defined two variables: : the mean atmospheric temperature and : the sales. They considered the month of July of this year in a random sample of 33 cities. For each city in the sample, let be the mean temperature in degrees Fahrenheit and the mean sales per day in dollars per 100,000 residents. The data are given below. A regression model was run, with as the dependent variable and as the independent variable. City City City 1 80.0 35.07 12 93.0 46.64 23 75.1 29.48 2 78.4 30.66 13 85.2 50.04 24 87.8 35.20 3 92.8 33.62 14 90.0 37.34 25 83.0 32.62 4 73.2 41.61 15 84.0 41.20 26 71.3 34.84 5 99.2 46.73 16 97.4 37.40 27 96.6 51.11 6 94.4 39.79 17 73.8 45.57 28 77.0 47.54 7 90.6 49.81 18 82.0 36.45 29 74.5 27.53 8 91.0 40.36 19 81.0 30.25 30 95.0 49.01 9 91.5 43.83 20 86.0 34.22 31 72.6 31.02 10 92.0 34.26 21 85.0 46.63 32 88.0 50.91 11 98.3 38.47 22 80.3 43.55 33 81.5 47.24 Question 1 Find the estimated regression equation for this sample.
Freshcrim specializes in the sales of ice cream from street trolleys in the centers of many cities. Some factors that may determine the sales of ice cream are: the atmospheric temperature, the location of the trolley, the rain and the humidity. However, there exists a hypothesis that the sales of ice cream during the summer are significantly correlated only with atmospheric temperature. They defined two variables: : the mean atmospheric temperature and : the sales. They considered the month of July of this year in a random sample of 33 cities. For each city in the sample, let be the mean temperature in degrees Fahrenheit and the mean sales per day in dollars per 100,000 residents. The data are given below. A regression model was run, with as the dependent variable and as the independent variable.
|
City |
|
City |
|
City |
||||||
|
1 |
80.0 |
35.07 |
|
12 |
93.0 |
46.64 |
|
23 |
75.1 |
29.48 |
|
2 |
78.4 |
30.66 |
|
13 |
85.2 |
50.04 |
|
24 |
87.8 |
35.20 |
|
3 |
92.8 |
33.62 |
|
14 |
90.0 |
37.34 |
|
25 |
83.0 |
32.62 |
|
4 |
73.2 |
41.61 |
|
15 |
84.0 |
41.20 |
|
26 |
71.3 |
34.84 |
|
5 |
99.2 |
46.73 |
|
16 |
97.4 |
37.40 |
|
27 |
96.6 |
51.11 |
|
6 |
94.4 |
39.79 |
|
17 |
73.8 |
45.57 |
|
28 |
77.0 |
47.54 |
|
7 |
90.6 |
49.81 |
|
18 |
82.0 |
36.45 |
|
29 |
74.5 |
27.53 |
|
8 |
91.0 |
40.36 |
|
19 |
81.0 |
30.25 |
|
30 |
95.0 |
49.01 |
|
9 |
91.5 |
43.83 |
|
20 |
86.0 |
34.22 |
|
31 |
72.6 |
31.02 |
|
10 |
92.0 |
34.26 |
|
21 |
85.0 |
46.63 |
|
32 |
88.0 |
50.91 |
|
11 |
98.3 |
38.47 |
|
22 |
80.3 |
43.55 |
|
33 |
81.5 |
47.24 |
Question 1
Find the estimated regression equation for this sample.
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