Question

# Ten salespeople were surveyed and the average number of client contacts per month, x, and the...

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.

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)

THIS IS A 100% VALID ANSWER

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