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 - bMX = 72.7 - (6.14*45.6) = -207.25731

ŷ = 6.13941X - 207.2573

(C)

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