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# Equation of line of regression

The store manager is under impression that his sales people do more business if they score higher on the social skills test which was administered this year. 5 victims were selected at random. Below, the results are X =test score, Y =weekly sales in \$1000.

X (score) Y (sales)

4 4

5 6

3 5

6 7

10 7

a) Find the correlation coefficient for the relationship between test results and sales

b) What percent of the total change in "Y" is based solely on changes in "X"?

c) Conduct a test to prove the hypothesis that there is a correlation between "X" and "Y". Use .05 level of significance.

d) Find the regression equation for test scores vs. weekly sales

e) Find the standard error of the estimate

#### Solution Preview

a)
&#8721;x = 28; &#8721;y =29 ; &#8721;xy =173; &#8721;x Ë?2 = 186; &#8721;yË?2= 175
_ _
x = 28/5 = 5.6 ; y = 29/5 = 5.8 ;
&#963;x = &#8730; (186/5 - 5.6*5.6 ) = &#8730;(37.2 - 31.36) = 2.416
&#963;y = &#8730; (175/5 - 5.8*5.8 ) = &#8730;(35 - 33.64) = 1.166
r = (173/5 - 5.8*5.6) / ...

#### Solution Summary

The equation of line of regression

\$2.19