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Equation of line of regression

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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

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The equation of line of regression

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a)
∑x = 28; ∑y =29 ; ∑xy =173; ∑x Ë?2 = 186; ∑yË?2= 175
_ _
x = 28/5 = 5.6 ; y = 29/5 = 5.8 ;
σx = √ (186/5 - 5.6*5.6 ) = √(37.2 - 31.36) = 2.416
σy = √ (175/5 - 5.8*5.8 ) = √(35 - 33.64) = 1.166
r = (173/5 - 5.8*5.6) / ...

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