Chapter 1 Regression And Correlation

ASIA PACIFIC UNIVERSITY OF TECHNOLOGY AND INNOVATION
Degree Level 1
Quantitative Skills
Correlation & Regression
Intake :
Lecturer :
Date Assigned :
Date Due :

1. Suppose that a random sample of five families had the following annual income and savings.

Income (X)
Savings (Y)
(£’000)
(£’000)
8
0.6
11
1.3
9
1.0
6
0.7
5
0.3

(a) Obtain the least square regression equation of savings (Y) on income (X) and plot the regression line on a graph. (b) Estimate the savings if the family income is £ 7000.

2. As part of an investigation into levels of overtime working, a company decides to tabulate the number of orders received weekly and compare this with the total weekly overtime worked to give the following: Week number
1
2
3
4
5
6
7
8
9
10
Orders received
83
22
107
55
48
92
135
32
67
122
Total overtime
38
9
42
18
11
30
48
10
29
51

Use the method of least squares to obtain a regression line that will predict the level of total overtime necessary for 100 orders

3. The following data show weekly prices and also sales of a mail order product over a two months period. Price (£)
Sales
8.99
496
9.50
465
9.99
482
10.50
459
10.99
408
11.50
382
11.99
315
12.50
363
12.99
309

(a) Plot this data on an appropriate labelled scatter diagram. (b) Calculate the product moment correlation coefficient. (c) Obtain the least square regression equation and plot the regression line on your graph. (d) Comment on your results.

4. (a) Draw a scatter diagram of about 10 points to illustrate the following degree of linear correlation. (i) no correlation (ii) weak positive correlation (iii) Perfect positive correlation
(iv) moderately strong negative correlation.

(b) The data below shows the appraised value and area of home for a sample of seven homes. Area (x) value (y)
(‘000 square feet )
($’000)
1.8
100
1.6
96
2.5
151
2.0
121
1.2
83
1.5
94
2.4
140

(i) Calculate the product moment