4.) A set of n=25 pairs of scores (X and Y values) produces a regression equatio

Question

4.) A set of n=25 pairs of scores (X and Y values) produces a regression equation of Y= 3X – 2. Find the predicted Y value for each of the following X scores: 0, 1, 3, -2.

6.) In general, how is the magnitude of the standard error of estimate related to the value of the correlation?

8.) For the following data:

            a. Find the regression equation for predicting Y from X.

b. Calculate the Pearson correlation for these data. Us r2 and SSY to compute SSresidual and the standard error of estimate for the equation.

X

Y

1

2

4

7

3

5

2

1

5

14

3

7

12.) A professor obtains SAT scores and freshman grade point averages (GPAs) for a group of n = 15 college students. The SAT scores have a mean of M = 580 with SS = 22,400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84.

Find the regression equation for predicting GPA from SAT scores.

What percentage of the variance in GPAs is accounted for by the regression equation? (Compute the correlation, r, then find r2.)

c. Does the regression equation account for a significant portion of the variance in GPA? Use = .05 to evaluate the F-ratio.

X

Y

1

2

4

7

3

5

2

1

5

14

3

7

Explanation / Answer

Question 4:

Solution:

A set of n=25 pairs of scores (X and Y values) produces a regression equation of Y= 3X – 2.

The predicted Y value for each of the following X scores: 0, 1, 3, -2. :

For X=0

Y=3*0-2 = -2

For X=1

Y= 3*1-2 =1

For X=3

Y=3*3-2 =7

For X = -2

Y=3*-2 -2 = -8

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