Chapter 16 Predicting Who’ll Win the Super Bowl:

Using Linear Regression

Part IVSignificantly Different:

Using Inferential Statistics

What you will learn in Chapter 16

How prediction works and how it can be used in the social and behavioral sciences

How and why linear regression workspredicting one variable from another

How to judge the accuracy of predictions

The usefulness of multiple regression

What is Prediction All About?

Correlations can be used as a basis for the prediction of the value of one variable from the value of anotherCorrelation can be determined by using a set

of previously collected data (such as data on variables X and Y)

calculate how correlated these variables are with one another

use that correlation and the knowledge of X to predict Y with a new set of data

Remember…

The greater the strength of the relationship between two variables (the higher the absolute value of the correlation coefficient) the more accurate the predictive relationship

Why???The more two variables share in common

(shared variance) the more you know about one variable from the other.

The Logic of PredictionPrediction is an activity that computes

future outcomes from present onesWhat if you wanted to predict college GPA

based on high school GPA?

Scatter Plot

Regression LineRegression line – reflects our best guess as

to what score on the Y variable would be predicted by the X variable.Also known as the “line of best fit.”

Prediction of Y given X = 3.0

Error in PredictionPrediction is rarely perfect…

Drawing the World’s Best Line

Linear Regression FormulaY=bX + a

Y = dependent variablethe predicted score or criterion

X = independent variablethe score being used as the predictor

b = the slope direction and “steepness” of the line

a = the interceptpoint at which the line crosses the y-axis

Slope & Intercept

Slope – calculating b

Intercept – calculating a

2 2

( / )

[( ) / ]

XY X Y nb

X X n

Y b Xa

n

How Good Is Our Prediction?

Standard error of estimate the measure of how much each data point

(on average) differs from the predicted data point or a standard deviation of all the error scores

The higher the correlation between two variables (and the better the prediction), the lower the error will be

Using the ComputerSPSS and Linear Regression

SPSS Output

What does it all mean?

SPSS Scatterplot

The More Predictors the Better? Multiple Regression

Multiple Regression FormulaY = bX1 + bX2 + a

Y = the value of the predicted scoreX1 = the value of the first independent

variableX2 = the value of the second independent

variableb = the regression weight for each variable

The BIG Rule…

When using multiple predictors keep in mind...Your independent variables (X1,, X2 ,, X3 , etc.)

should be related to the dependent variable (Y)…they should have something in common

However…the independent variables should not be related to each other…they should be “uncorrelated” so that they provide a “unique” contribution to the variance in the outcome of interest.

Glossary Terms to Know

Regression lineLine of best fit

Error in predictionStandard error of the estimate

CriterionIndependent variable

PredictorDependent variable

Y primeMultiple Regression