# Psychological Statistics- Regression

1. Explain the difference between a standard deviation and the standard error of estimate

2. Given the regression line in the graph below for question #11 on pg. 160. (scan 3 file attachment)

(part 2) draw the regression line for a = -2 and b = -.24

3. To determine the relationship between speed and precision in driving, an investigator asks several people to drive an obstacle course. The people are instructed to drive as fast as possible, while at the same time hitting as few obstacles as possible. Below are the results for 6 people:

X = number of minutes taken to complete the obstacle course

Y = number of obstacles hit by driver

{ X Y }

{ 3 8 }

2 9

7 5

9 3

5 6

1 7

a) construct the scatterplot (with "number of minutes..." on the x-axis)

b) compute the regression constants (a and b) for the prediction of number of hits from number of minutes, and write the regression equation (see example on p.146 of your book; 8th ed) (attachment scan 7)

c) Plot the regression line on the scatterplot you made in (a) (see example on p. 149 of your book; 8th ed) (attachment scan 4)

d) Using the regression equation from (b), what is the predicted number of hits if the driver completes the course in 2 minutes?

e) describe the relationship between the two variables in this study.

f) Compute the standard error of the estimate. What does it tell you in this case? (see example on pp. 155-156 in your book; 8th ed) (attachment scan 5-6)

#### Solution Preview

Please see the answers in the attached Excel File.

1. Explain the difference between a standard deviation and the standard error of estimate

"Standard deviation is a measure of dispersion of the values in the data set around the mean value. Higher the standard deviation more the values are scattered around the mean value.

The standard error of the estimate is a measure of the accuracy of predictions made with a regression line. The more is the standard error, less is the accuracy of prediction.

"

2. Given the regression line in the graph below for question #11 on pg. 160. (scan 3 file attachment)

Equation of the regression line Y = a + b X

The regression line passes through (1,5) and (5,2)

Point 1 x1= 1 y1= 5

Point 2 x2= 5 y2= 2

b= slope= (y2-y1)/ (x2-x1)= -0.75 =(2-5)/(5-1)

The regression line passes through Point 1

Substituting the values of x1 and y1

5 = a -0.75 x 1

or

5 = a -0.75

or a= 5.75

Y = 5.75 - 0.75 X

(part 2) draw the regression line for a = -2 and b = -.24

a= -2

b= -0.24

Y = -2 - 0.24 X

We need to plot two points to get a straight line

a is the Y -intercept

Thus first point is x1= 0 y1= -2

For second point we take x2= 1

For this point y2= -2.24 = -2 - 0.24 X ...

#### Solution Summary

Questions on regression, scatter plot, standard error etc.