Market research firm is interested in measuring whether there is relationship between age and consumption patterns of particular product. They sample fifteen individuals and ask their age and amount they spent on that product in prior year. Figures are as follows:
|
Individual
|
Age
|
Amount spent
|
|
1
|
25
|
68
|
|
2
|
47
|
46
|
|
3
|
58
|
31
|
|
4
|
37
|
56
|
|
5
|
59
|
35
|
|
6
|
21
|
81
|
|
7
|
55
|
45
|
|
8
|
43
|
38
|
|
9
|
47
|
42
|
|
10
|
24
|
68
|
|
11
|
61
|
28
|
|
12
|
55
|
18
|
|
13
|
29
|
65
|
|
14
|
50
|
31
|
|
15
|
39
|
55
|
Questions:
i) Compute Pearson's correlation coefficient between age and amount spent on this particular product.
ii) Test this correlation for statistical significance (at a 5% significance level).
iii) Estimate linear regression to study relationship between age and amount spent on this product.
iv) If individual was 40 years old, what would you forecast his/her amount spent on this product to be for prior year?
v) Comment on any potential problems there might be with this regression.