Question

The director of an alumni association for a small college wants to determine whether there is any type of relationship

between the amount of an alumnus's contribution (in dollars) and the years the alumnus has been out of school.

Use the Data Analysis toolpack: Correlation and Regression and answer the questions below.

Years Contribution

1 500

5 154

3 300

10 61

7 75

6 80

Give the following:

correlation coefficient:

is there a significant correlation between variables?

Equation of the Regression line

a

b

Predict the amount of contribution if the alumnus has been out of school for 4 years.

Answer 1

a) Correlation coefficient:

The provided data are shown in the table below

X	Y
1	500
5	154
3	300
10	61
7	75
6	80

Also, the following calculations are needed to compute the correlation coefficient:

	X	Y	X*Y	X2	Y2
	1	500	500	1	250000
	5	154	770	25	23716
	3	300	900	9	90000
	10	61	610	100	3721
	7	75	525	49	5625
	6	80	480	36	6400
Sum =	32	1170	3785	220	379462

Therefore, based on this information, the sample correlation coefficient is computed as follows

b)

Hence there is a significant correlation between the variables

c)

the following is calculated:

Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows:

Therefore, we find that the regression equation is:

d)

When X = 4 then

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