Your company has been granted an exclusive license to sell ice cream. No one has ever sold ice cream here before, so you have no idea what the demand will look like. You suspect that people like to buy more ice cream on hotter days, but you are very unsure about what price you should charge to maximize your profit.
Over your first season selling ice cream, you vary your price each week for the 10 weeks your license allows you to operate. You collect data including price you charged that week (giving you 7 data points at each price), the high temperature for that day, and the average number of cones sold per hour each day.
You have paid a fixed fee of $10,000 to the state which covers materials (both the costs of the cones and the fixed costs associated with the food truck) to supply the ice cream cones that doesn’t vary depending on how many units are sold. A single employee, making $15/hour can handle up to 40 cones per hour, while a second employee would bring your maximum production up to 100 cones per hour.
Instructions
Use the data below perform a multiple regression analysis, with Sales per Hour as your dependent variable and ‘Price’ and ‘Avg Temp’ as independent variables.
Q5) The State is considering raising the license fee. Assuming you can operate 7 days a week for the 10 week season, and labor is your only direct expense (the contract covers the costs of cones outside of labor). If your company wishes to enter the contract at any positive profit (any profit > $0), what is the maximum amount your company should be willing to pay?
Ice cream sales data
Day Sales per hour Price Avg Temp
1 30.65 0.75 77
2 30.55 0.75 92
3 25.89 0.75 74
4 31.84 0.75 91
5 24.09 0.75 67
6 27.81 0.75 92
7 25.27 0.75 73
8 28.21 1.50 92
9 28.15 1.50 89
10 23.07 1.50 79
11 31.15 1.50 93
12 19.76 1.50 70
13 26.00 1.50 75
14 29.37 1.50 91
15 28.47 1.25 95
16 23.82 1.25 71
17 24.11 1.25 76
18 29.19 1.25 90
19 28.73 1.25 91
20 24.20 1.25 91
21 24.91 1.25 77
22 21.76 2.00 87
23 21.15 2.00 71
24 20.31 2.00 73
25 16.54 2.00 67
26 20.18 2.00 69
27 23.53 2.00 93
28 21.01 2.00 77
29 26.85 1.00 79
30 27.12 1.00 81
31 28.93 1.00 74
32 22.91 1.00 65
33 27.33 1.00 81
34 24.27 1.00 80
35 26.63 1.00 81
36 17.93 2.25 69
37 20.65 2.25 90
38 15.97 2.25 74
39 23.55 2.25 92
40 20.25 2.25 67
41 19.13 2.25 73
42 19.72 2.25 90
43 30.66 0.50 82
44 28.68 0.50 92
45 24.97 0.50 71
46 34.21 0.50 94
47 25.64 0.50 71
48 31.66 0.50 93
49 26.87 0.50 72
50 18.42 1.75 69
51 25.74 1.75 79
52 20.36 1.75 72
53 22.15 1.75 70
54 28.66 1.75 85
55 26.42 1.75 94
56 24.34 1.75 74
57 21.93 1.35 73
58 23.51 1.35 67
59 26.99 1.35 82
60 32.10 1.35 86
61 25.21 1.35 84
62 27.59 1.35 93
63 19.63 1.35 69
64 23.63 1.65 81
65 20.76 1.65 66
66 24.57 1.65 79
67 29.27 1.65 91
68 24.32 1.65 68
69 19.85 1.65 66
70 25.29 1.65 91
Answer:-
| Coefficientsa | ||||||||
| Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | 95.0% Confidence Interval for B | |||
| B | Std. Error | Beta | Lower Bound | Upper Bound | ||||
| 1 | (Constant) | 12.348 | 2.277 | 5.423 | .000 | 7.804 | 16.893 | |
| Price | -4.687 | .475 | -.602 | -9.859 | .000 | -5.635 | -3.738 | |
| TEMP | .239 | .026 | .560 | 9.164 | .000 | .187 | .292 | |
| a. Dependent Variable: SalesHour | ||||||||
A general equation : Y= a+ b1X1 + b2X2 ... bnXn
For this
dependent variable(Y) = Sales/hour (S)
Independent Variables - Price (P) , Temperature (T)
From the regression analysis the equation will be as follows :
S = 12.348 + (-4.687)P + (0.239)T
The negative sign for the co-efficient of P signifies an inverse relationship between sales and price. So if price increase the sales will fall and vice-versa.
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