1.A company that manufacturers wooden products (e.g. garden furniture, ladders, benches) regularly maintains its lathe machines, which are used for cutting and shaping components. The manager would like to know whether the cost of machine maintenance is related to the age of the machines. For a random sample of 12 lathe machines in the company's factory, the annual maintenance cost (in R100s) and age of each machine was recorded.

Machine

Age (years)

Annual cost (Rand)

1

4

45

2

3

20

3

3

38

4

8

65

5

6

58

6

7

50

7

1

16

8

1

22

9

5

38

19

2

26

11

4

30

12

6

35

(i)Identify the independent variable and the dependent variable.

(ii)Show the data graphically in a scatter plot. What relationship is observed?

(iii)Calculate the correlation coefficient between the age of lathe machines and their annual maintenance costs. Comment on the strength of the association.

(iv)Is the correlation statistically significant? Test at the 5% significance level. What conclusion can be drawn?

(v)Use the method of least squares to find the best fitting line between the age of lathe machines and their annual maintenance costs.

(vi)Interpret the meaning of the regression coefficient (b1) of the independent variable.

(vii)What is the expected average maintenance cost of a lathe machine that is five years old?