A manager wishes to determine the relationship between the n

A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the sales representative travels per month and the amount of sales (in thousands of dollars) per month. The Z-scores for both variables are shown below. Miles: -0.98 -0.77 0.70 0.07 0.28 1.75 -0.77 -1.19 0.91 Sales: -1.14 -1.07 0.62 0.02 0.13 -0.02 -0.50 -0.24 2.20 What is the correlation coefficient? 0.632 0.561 0.717 0.791

Solution

Miles(X): -0.98 -0.77 0.70 0.07 0.28 1.75 -0.77 -1.19 0.91 0 sales(Y): -1.14 -1.07 0.62 0.02 0.13 -0.02 -0.5 -0.24 2.2 0 X²:.9604 .5929 .49 .0049 .0784 3.0625 .5929 1.4161 .8281 8.0262 Y²:1.2996 1.1449 .3844 .0004 .0169 .0004 .25 .0576 4.84 7.9942 X*Y:1.1172 .8239 .434 .0014 .0364 -.035 .385 .2856 2.002 5.0505 cov(X,Y)=(1/n)XY- (Xbar*Ybar)=5.0505/9-0=.5612 , ²_X=(1/n)X²-(Xbar)²=8.0262/9-0=.8918, ²_Y=(1/n)Y²-(Ybar)²=7.9942/9-0=.8882. Correlation coefficient(r)=cov(X,Y)/(²_X*²_Y)=(.5612)/((.8918*.8882))=.5612/.89=.6306