A market research firm is interested in assessing whether there is the relationship between age and consumption patterns of particular product. They sample 15 individuals and ask their age and amount they spent on that product in previous year. The 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
|
Required
- Compute Pearson's correlation coefficient between age and amount spent on this specific product.
- Test this correlation for statistical significance (at a 5% significance level).
- Estimate the linear regression to analyze the relationship between age and amount spent on this product.
- If an individual was 40 years old, what would you predict his or her amount spent on this product to be for previous year?
- Comment on any potential problems there may be with this regression.