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Regression Analysis

Unit: Quantitative Analysis

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November 2020

 1 Questions
Question 3b
​ ​ ​​The production manager of Sweet Ltd. is concerned with the fluctuating indirect labour cost in relation to the labour hours worked by the employees.

The following data was collected for the past 12 months.

Month
Labour hours
"000"
Indirect labour cost
"000" 
January
February
March
April
May
June
July
August
September 
October
November
December
48
68
94
82
46
78
96
60
72
62
88
68
963
752
1,032
1,316
710
1,180
1,456
770
1,004
1,211
917
1,190

Required:
Using the ordinary least squares method:
(i).   Formulate the indirect cost function.
(ii).  Compute the indirect labour cost for 120 labour hours.
(iii).  Calculate the coefficient of determination.


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November 2019

 2 Questions
Question 3b
​ ​A small business is interested in establishing the relationship between the number of hits on its website (measured by number of visitors that have used the main menu) and the amount spent in website promotion (in Sh. "000"). 

The table below gives the figures for the last six months:​

Month
Website hits
Website promotion
(Ksh. "000")
1
24
1.0
2
25
1.2
3
56
1.6
4
54
1.4
5
55
1.2
6
58
1.8

Required:
(i) Illustrate, using a graph, the number of website hits against the amount spent in website promotion. Comment on any relationship between website hits and the extent of promotion. 
(ii) Calculate the correlation coefficient and give an interpretation to its value. 
(iii) Determine the regression line.


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Question 5c
​​John Wekesa is the manager at Mikate Bakers Ltd. He intends to establish the cost of each bread. He gathers the following data on the total cost of each day's production for the last 10 days as shown in the table below:

Day
Number of units of
bread (in hundreds) 
Total cost
(Sh."000")
1
45
46
2
42
43.2
3
55
46.6
4
43
48
5
60
56.4
6
40
44.8
7
48
46.2
8
53
50.6
9
36.6
40.2
10
34
33

Required: 
(i) The total cost function using the least squares method. 
(ii) If each bread is sold at Sh.50, predict the break-even number of units of bread.


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May 2019

 1 Questions
Question 4c
​ ​​The table below shows the number of years of experience of ten salespersons and the respective mean monthly sales realised by the salespersons.
​​
Salesperson
Years of experience
Mean monthly sales (Sh.)
1
6
180,000
2
4
150,000
3
2
  80,000
4
10
500,000
5
7
190,000
6
4
100,000
7
6
200,000
8
7
220,000
9
12
600,000
10
8
200,000

Required: 
 (i) The coefficient of correlation. Interpret your result. 
(ii) Using ordinary least squares method, predict the mean monthly sales that would be realised by a salesperson having 15 years of experience.


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November 2018

 1 Questions
Question 3c
​​The following data were obtained from the records of a certain company, relating to the year 2018:

Month
Total overhead costs - Y (Sh.)
Direct labour hours - X
January
14,250
856
February
13,000
536
March
13,000
640
April
12,500
600
May
13,250
680
June
13,750
808

Required:
(i) The least squares regression function relating the direct labour hours to the total overhead cost. 
(ii) The coefficient of determination. 
(iii) Comment on the results obtained in (c) (ii) above.


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December 2017

 2 Questions
Question 3a
​​ Distinguish between "regression analysis" and "correlation analysis".


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Question 3c
​ ​ ​ ​​The following exponential function represents the advertising cost of a certain small enterprise:

Y = abx

Where:  y is the advertising cost in thousands of shillings 
             a, b are constants over a period of seven years. 
             x is the period under consideration.

The actual advertising cost of the enterprise over a seven year period is given as follows:

Year
1
2
3
4
5
6
7
Advertising cost (Sh. "000")
32
47
65
92
132
190
275

Required:
 (i) The advertising cost function of the enterprise, using the normal equation. 
(ii) The advertising cost of the enterprise in year 8.


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May 2017

 1 Questions
Question 1d
​ ​ ​​Market Intelligence Research Limited carried out a study on nine households to determine the monthly income levels and the amount of expenditure incurred by the households. The results of the study are as shown below:

Monthiy Income (Sh. "000")
15
6
9
3
20
11
14
10
12
Expenditure (Sh.)
2,000
200
500
500
2,500
800
1,500
1,500
1,600

Required:
 (i) The least squares regression function relating the monthly income and expenditure incurred by the households. Interpret your results. 
 (ii) The expenditure incurred by a household whose monthly income is Sh.30,000.


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November 2016

 1 Questions
Question 2c
​ ​​

The following data show results of a regression run on the variations in labour cost as a function of labour hours worked in a certain company:

Regression statistics

R-squared
X1
Multiple R
X2
Standard error
0.7320
Observations
24

ANOVA

Degrees of freedom (DF) Sum of squares (SS) Mean square (MS) F-ratio Significance F
Regression
 X3
 0.029
       0.029
 X5
 0
Residual or error
 22
         X4     
 0.000455
Total
 23
  0.04

Coefficients

Coefficients Standard error t-statistic P-value
Intercept
 0.077
 X6
 11.328
 0
Slope
 0.826
 0.103
 X7
 0

Required:

  1. The missing values of X1, X2, X3, X4, X5, X6, and X7.
  2. A 95 per cent confidence level of the labour hours worked.


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November 2015

 1 Questions
Question 3b
The table below relates to the number of units packaged by nine casual employees of Bidii Limited and the packaging time taken by each of the employees:

Number of units packaged
Time (seconds) 		14
230		 8
110		 9
130		 12
190		 6
109		 11
181		 10
154		 5
79		 10
144

Required:
(i) The regression line of packaging time against the number of units packaged.
(ii) The product moment correlation coefficient.
(iii) The standard error of estimate.
(iv) A 95 per cent interval estimate of the regression line.
(v) The packaging time interval for 7 units.


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Pilot September 2015

 1 Questions
Question 2b
​​A marketing firm employs part-time marketers. The hours worked and the earnings of ten such marketers are as shown below:

Marketer
Hours worked (x)
Earnings (Sh. “000”) (y)		1
20
5.5		2
30
7.4		3
48
11.0		4
39
9.3		5
28
7.2		6
14
4.3		7
60
13.5		8
50
12.0		9
62
14.0		10
43
10.0

Required:
(i) The least squares regression function relating the hours worked and earnings. Interpret your results.
(ii) The Spearman\\\'s rank correlation coefficient. Comment on your result.


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