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.

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.

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.

Your employee from the first season reports the following: “When we charged the higher prices last year, we had some people complaining. I don’t think we should charge any more than $2.75 for a cone.”

Calculate the price elasticity of demand if you charge $2.75 (still assuming an average temperature of 80 degrees). Based on this analysis, do you agree with your employee?

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

Answer:-

Coefficients^{a} |
||||||||

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.

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...

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...

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...

Using the accompanying Student Grades data, construct a scatter
chart for midterm versus final exam grades and add a linear
trendline. What is the model? If a student scores 7878 on the
midterm, what would you predict her grade on the final exam to
be?
Student
Midterm
Final Exam
1
75
64
2
85
91
3
80
68
4
88
83
5
76
60
6
67
80
7
78
74
8
95
94
9
67
61
10
93
87
11...

Student Grades
Student
Test
Grade
1
76
62
2
84
90
3
79
68
4
88
84
5
76
58
6
66
79
7
75
73
8
94
93
9
66
65
10
92
86
11
80
53
12
87
83
13
86
49
14
63
72
15
92
87
16
75
89
17
69
81
18
92
94
19
79
78
20
60
71
21
68
84
22
71
74
23
61
74
24
68
54
25
76
97...

Please note that for all problems in this course, the
standard cut-off (alpha) for a test of significance will be .05,
and you always report the exact power unless SPSS output states
p=.000 (you’d report p<.001). Also, remember when
hand-calculating, always use TWO decimal places so that deductions
in grading won’t be due to rounding differences.
Problem Set 1: (22 pts)
A teacher wanted to see if a new pedagogical approach was
beneficial to students, and if the effects vary...

This dataset contains consumer responses indicating the number
of times they had to send their product for repair and their
satisfaction with the repair process. Create a graph which can be
used to visually demonstrate the relationship between the two
columns of data. Ensure that the chart is professional with
appropriate titles, axis labels, etc. Note any observations you see
in your visualization (type these as sentences directly into an
Excel cell(s)).
Sample
Satisfaction Rating
Repair Requests
1
63%
13...

Your assignment is to do a detailed statistical analysis of the
data to be able to decide later what would be appropriate control
charts to monitor these variables.
The manager provides you data that the office has collected on
these two variables:
Time it takes since the patient checks-in until the patient
checks-out
Number of patients in the waiting room
Present a report to the manager with the results of the
statistical analysis of the data and your conclusions on...

Your assignment is to do a detailed statistical analysis of the
data to be able to decide later what would be appropriate control
charts to monitor these variables.
The manager provides you data that the office has collected on
these two variables:
Time it takes since the patient checks-in until the patient
checks-out
Number of patients in the waiting room
Present a report to the manager with the results of the
statistical analysis of the data and your conclusions on...

(a) Construct a 99% confidence interval for the population
proportion who prefer your client's product.
(b) Would a 95% confidence interval for the same population
proportion be wider or narrower.
(c) The marketing director of your client's company states, "I
am almost certain that our product is preferred by at least 40% of
consumers". Based on your answer to part (a), do you agree with
him? Why or why not?
Consumer ID
Product Preference
1
Competitor
2
Client
3
Competitor...

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