The managing director of a company wants to find whether there is a relationship between units of a product produced and the profits in a period of 12 months. Month Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Units produced (X)‘000 2 3 5 8 11 10 12 15 17 18 20 24 Profits (Y) ‘000 3 5 8 11 13 14 16 20 22 24 26 30 i. Calculate the regression equation of the form Y = a + bX and hence estimate the value of the profits when 25,000 units are produced. ii. Calculate the regression equation of the form X = a + bY and hence estimate the value of the units produced when 27,000 in profits is made. iii. Calculate and both the Pearson correlation coefficient and coefficient of determination, interpret both and justify in this case why it would be prudent to rely on the coefficient of determination rather than Pearson in decision making.
The managing director of a company wants to find whether there is a relationship between units of a product produced and the profits in a period of 12 months.
|
Month |
Jan |
Feb |
Mar |
Apr |
May |
June |
July |
Aug |
Sept |
Oct |
Nov |
Dec |
|
Units produced (X)‘000 |
2 |
3 |
5 |
8 |
11 |
10 |
12 |
15 |
17 |
18 |
20 |
24 |
|
Profits (Y) ‘000 |
3 |
5 |
8 |
11 |
13 |
14 |
16 |
20 |
22 |
24 |
26 |
30 |
i. Calculate the regression equation of the form Y = a + bX and hence estimate the value of the profits when 25,000 units are produced.
ii. Calculate the regression equation of the form X = a + bY and hence estimate the value of the units produced when 27,000 in profits is made.
iii. Calculate and both the Pearson
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