Question # 1                                                                                                                    A well-known multinational FMCG produces more than fifty products and sells them in the market. Out of fifty products one is mineral water for drinking purpose and supplies different size pack bottles in the market. Product manager observed that, during hot days the sale of water is more as compared to the normal days.  He started the collection of data of weekly sale of water and the average weekly temperature. Product manager was interested in developing a relationship between sales and temperature; therefore, he discussed and shared the following data with you. sales 75 77 69 63 79 80 77 70 73 87 72 73 80 80 69 84 77 72 74 81 temperature 32 36 31 31 34 29 32 35 28 31 30 31 29 35 36 28 32 33 32 33   Sale is in thousand liters and temperature is in degree Celsius. Data is Normally distributed   You are required to determine the following information for some concrete decision:   Determine the statistical relationship between temperature and sale of water and interpret. How much change in sales if the temperature increases by two degrees? If for instance, the temperature becomes zero then how much sales will be? How much percent variation in sales due to temperature and due to other factors? Write the equation for the prediction of sales.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
icon
Concept explainers
Question

Question # 1                                                                                                                   

A well-known multinational FMCG produces more than fifty products and sells them in the market. Out of fifty products one is mineral water for drinking purpose and supplies different size pack bottles in the market. Product manager observed that, during hot days the sale of water is more as compared to the normal days.  He started the collection of data of weekly sale of water and the average weekly temperature.

Product manager was interested in developing a relationship between sales and temperature; therefore, he discussed and shared the following data with you.

sales

75

77

69

63

79

80

77

70

73

87

72

73

80

80

69

84

77

72

74

81

temperature

32

36

31

31

34

29

32

35

28

31

30

31

29

35

36

28

32

33

32

33

 

Sale is in thousand liters and temperature is in degree Celsius. Data is Normally distributed

 

You are required to determine the following information for some concrete decision:

 

  1. Determine the statistical relationship between temperature and sale of water and interpret.
  2. How much change in sales if the temperature increases by two degrees?
  3. If for instance, the temperature becomes zero then how much sales will be?
  4. How much percent variation in sales due to temperature and due to other factors?
  5. Write the equation for the prediction of sales.  

 

Expert Solution
Step 1

“Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.”

Let (X,Y) be the bivariate distribution where Y is the dependent and X is the independent variable. The line of regression is the line which gives the best estimate to the values of one variable for the specific value of the other variable. The line of regression is obtained by the principle of least square. The equation of the line of regression of Y on X is given as:

Y=a+bX

Here, a and b are constants obtained as:

a=i=1nyinb=xii=1nyixi2i=1n

Step 2

(1.) Let X denotes temperature and Y denotes sales. Here, n=20.

Calculation Table:

xi yi xi2 xiyi
32 75 1024 2400
36 77 1296 2772
31 69 961 2139
31 63 961 1953
34 79 1156 2686
29 80 841 2320
32 77 1024 2464
35 70 1225 2450
28 73 784 2044
31 87 961 2697
30 72 900 2160
31 73 961 2263
29 80 841 2320
35 80 1225 2800
36 69 1296 2484
28 84 784 2352
32 77 1024 2464
33 72 1089 2376
32 74 1024 2368
33 81 1089 2673
Total 1512 20466 48185

 

Step 3

Using above calculation table, we get

a=i=1nyin=151220=75.6b=xii=1nyixi2i=1n=4818520466=2.3544

steps

Step by step

Solved in 5 steps

Blurred answer
Knowledge Booster
Correlation, Regression, and Association
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman