Welcome to MM570Welcome to MM570Psychological StatisticsPsychological Statistics

Unit 4 SeminarDr. Bob Lockwood

Linear Regression and Prediction

• Assume that there is a tennis club that will let anyone play tennis but there is a flat fee for using the facility and then a per-hour fee for using the tennis courts.

• Now, this club tells us that the fee to use the club is $10.00 and the per-hour cost is $5.00.

• Can you calculate the cost of playing 2 hours of tennis?

• Can you estimate the cost to play 10 hours of tennis?

Linear Regression and Prediction• Now to do find out how much it will cost to play

tennis all you did was take $10 plus $5 times the number of hours, right?

• I might write this as Cost or criterion variable = rate or predictor variable (hours) +base cost; which looks a lot like: • Ŷ = a +(b)(x) {Linear Prediction Rule or the Regression

Line}

The formula to get a and b look like this:

• b = ∑[(X-Mx)(Y-My)]/ SSx

• a = My – (b)(Mx)

The Linear Prediction Rule• Regression constant (a)

• Predicted raw score on criterion variable when raw score on predictor variable is 0

• Intercept of the regression line

• Regression coefficient (b)• How much the predicted criterion variable

increases for every increase of 1 unit on the predictor variable

• Slope of the regression line

Drawing the Regression LinePage 495

1. Draw and label the axes for a scatter diagram

2. Figure predicted value on criterion variable for a low value on predictor variable – mark the point on graph

3. Repeat step 2. with a high value on predictor variable

4. Draw a line passing through the two marks

Drawing the Regression Line

Least Squared Error Principle

• Used to determine the one best prediction rule

• Error = Actual score minus the predicted score

• The best prediction rule has the smallest sum of squared errors

22 )ˆ( YYError

Multiple Regression

• Multiple regression prediction models• Each predictor variable has its own regression

coefficient• Multiple regression formula with three

predictor variables:

))(())(())(( 332211 XbXbXbaY

You really do not want to do this math!

Limitations of Regression

• Regression inaccurate if• Correlation is curvilinear• Restriction in range is present• Unreliable measures are used

Does this look familiar?

Using SPSS Bivariate Prediction Rule

Enter the scores into two columns of the Data Window Analyze Regression Linear and drag the dependent variable and drag the independent variable Statistics Descriptives Continue OK

SPSS Bivariate Prediction Rule 1

SPSS Bivariate Prediction Rule 2

SPSS Bivariate Prediction Rule 3

Using SPSS Multiple Prediction Rule

Enter the scores into three columns of the Data Window Analyze Regression Linear and drag the dependent variable and drag the independent variables Statistics Descriptives Continue OK

SPSS Multiple Prediction Rule 1

SPSS Multiple Prediction Rule 2

• SPSS Multiple Prediction Rule 3

• SPSS Multiple Prediction Rule 4

• SPSS Multiple Prediction Rule 5

QUESTIONS??