Question

Part (a)Using the Experience and Income xlsx file, determine the sample correlation coefficient between the annual salary and the job market experience variables.

Part (b)Interpret the sample correlation coefficient you found in part (a)

Part (c)If we regressed income on experience, what share of the variation in income could be explained by the variation in experience? Explain how you found your answer.

Individuals' Annual Salaries and Job Market Experience
Annual Salary	Years of Job Market Experience
83601	18
29736	47
50235	12
22133	10
21994	24
29390	18
17694	38
26795	44
19981	54
14476	3
19452	3
28168	17
19306	34
13318	25
25166	10
18121	18
13162	6
32094	14
16667	4
50171	39
31691	13
36178	40
15234	4
16817	26
22485	22
30308	10
11702	6
11186	0
12285	42
19284	3
11451	8
57623	31
25670	8
83443	5
49974	26
46646	44
31702	39
13312	9
44543	10
15013	21
33389	22
60626	7
24509	15
20852	38
30133	27
31799	25
16796	14
20793	6
29407	19
29191	9
15957	10
34484	28
35185	12
26614	19
41780	9
55777	21
15160	45
66738	29
33351	4
33498	20
29809	29
15193	15
23027	34
75165	12
18752	45
83569	29
32235	38
20852	1
13787	4
34746	15
17690	14
52762	7
60152	38
33461	7
13481	7
9879	28
16789	6
31304	26
37771	5
50187	24
39888	5
19227	15

Answer 1

(A) Enter the data values into column A and column B of excel from cell 1 to 83, where first cell labels.

Using CORREL function in excel and selecting annual salary as array1 and years of job market experience as array2, we get

=CORREL(A2:A83,B2:B83)

= 0.0833

(B) Correlation coefficient calculated in part (A) is r = 0.0833. This value is very close to 0, which means that there is very weak positive relationship between the annual salary and years of job market experience. There is positive relationship because the correlation coefficient is positive, but very small in magnitude.

(C) We know that coefficient of determination tells us about the percent of variation in dependent variable that is explained by independent variable and coefficient of determination or r squared value is given as

Coefficient of determination = r^2

setting r = 0.0833

we get, coefficient of determination = 0.0833^2 = 0.0069

this means that only 0.69% variation in income could be explained by the variation in experience.