Question

Ten salespeople were surveyed and the average number of client contacts per month, x, and the sales volume, y (in thousands), were recorded for each: X 40 42 44 40 41 46 50 48 50 55 Y 50 55 42 45 30 80 90 95 110 130

a) Find the correlation coefficient r.

b) Find the regression equation

c) Construct the scatter plot and graph the regression equation.

Answer #1

SOLUTION:-

(A)

*X Values*

∑ = 456

Mean = 45.6

∑(X - Mx)2 = SSx = 232.4

*Y Values*

∑ = 727

Mean = 72.7

∑(Y - My)2 = SSy = 9886.1

*X and Y Combined*

*N* = 10

∑(X - Mx)(Y - My) = 1426.8

*R Calculation*

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = 1426.8 / √((232.4)(9886.1)) = 0.9413

r = 0.9413

This is a strong positive correlation, which means that high X variable scores go with high Y variable scores

(B)

Sum of *X* = 456

Sum of *Y* = 727

Mean *X* = 45.6

Mean *Y* = 72.7

Sum of squares (*SSX*) = 232.4

Sum of products (*SP*) = 1426.8

Regression Equation = ŷ = *bX* + *a*

*b* = *SP*/*SSX* = 1426.8/232.4 =
6.13941

*a* = MY - *b*MX = 72.7 - (6.14*45.6) =
-207.25731

ŷ = 6.13941*X* - 207.2573

(C)

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