# Regression equation, predicted Y value, Pearson correlation

22. For the following data:

X y

1 2

4 7

3 5

2 1

5 14

3 7

a. Find the regression equation predicting Y from X.

b. Use the regression equation to find a predicted Y from each X.

c. Find the difference between actual Y value and the predicted Y value for each individual, square the differences, and add the squared values to obtain SS residual.

d. Calculate the Pearson correlation for these data. Use r2 and SSy to compute SSresidual with Equation 15.18. You should obtain the same value as in part c.

(Equation 15.18 - Unpredicted variability = SSresidual= (1-r2)SSy)

Use the formulas to obtain the slope b and intercept a for part a. Then just follow the simple instructions in parts b - c. For part a you should get estimated regression line as Y hat = 3X - 3

#### Solution Summary

A Complete, Neat and Step-by-step Solution is provided in the attached Excel file.