2.) The regression equation is intended to be the “best fitting” straight line f

Question

2.) The regression equation is intended to be the “best fitting” straight line for a set of data. What is the criterion for “best fitting”?

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.

a. Find the regression equation for predicting GPA from SAT scores.

b. 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

Answer to 1st question:

2)

When we look at a scatter plot of two variables, if we could draw a straight line with a ruler close to most of the data, we would be able to predict the value of one variable based on a value of the other.

Most statistical packages use the method of least squares. This method uses the data to find the line of best fit by minimizing the sum of the squares of the distances of the data points to the line. The squares of the distances are used since the distance might be a negative number, but the square of the distance of the point to the line will be positive. Examples of the distance of the point to the line is indicated by the red lines below. The equation of this line of best fit can be found from the data.

Through this procedure an estimateof the equation of the line is sought. An estimate is not about being exactly correct. It provides what some people refer to as a "ballpark figure" - something that is near to and could be, but is not expected to be, exact.

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