Question

The director of an alumni association wants to determine whether there is any type of relationship between the amount of an alumni's contribution (in dollars) and the number of years the alumnus has been out of school. Based on the data below, compute the value of the correlation coefficient between the number of years and the amount of the contribution.

Years x 1 3 4 10 9 7

Contribution y 630 180 210 30 90 90

Answer 1

Solution:

The formula to find correlation coefficient is given below.

where n=6=number of observations

Now let us find the values as per the above formula.

Years(x)	Contribution (y)	xy	x2	y2
1	630	630	1	396900
3	180	540	9	32400
4	210	840	16	44100
10	30	300	100	900
9	90	810	81	8100
7	90	630	49	8100
x=34	y=1230	xy=3750	x2=256	y2=490500

Substituting the values from the table in the given formula,

r=[(6*3750)-(34*1230)] / [(6*256)-342)]*[(6*490500)-12302]

=-19320/(380*1430100)

=-19320/23311.76

=-0.82877

=-0.83

The value of the correlation coefficient between the number of years and the amount of the contribution is -0.83.

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