Question

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. That data is below

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 to perform a multiple regression analysis, with Sales per Hour as your dependent variable and ‘Price’ and ‘Avg Temp’ as independent variables.
Q1) You think that quantity demanded is a function of price and the weather, with higher temperatures shifting demand to the right. That would make the general form of the demand function is Qd = f(P, T) where P is the price of ice cream cones and T is average temperature. Based on your regression analysis, write out your estimate of the specific form of the demand function for ice cream.
I’m just looking for an equation here.

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 1

  

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.