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Multiple Regression is an analytical tool built upon Multiple Correlation. Its goal is the prediction of scores on a single criterion variable using a combination of several predictor variables.
Scenario: Data was collected on ten students exam marks for French, English, Maths, and Statistics. Their IQ was also measured using a standard test.
Prediction: Students exam marks in the four subjects will reliably predict their IQ scores.
Null-Prediction: Students exam marks in the four subjects will not reliably predict their IQ scores.
Open SPSS and enter the following data:-
This shows that the four predictors explain 61.2% of total variance.
Is there a significant Regression Equation?
Is there one variable that is a reliable predictor of IQ?
Which exam result was the best predictor of IQ?
The greatest Beta value would indicate this. The Beta weight tells us the number of Standard Deviations change on the Dependent Variable that will be produced by a change of one Standard Deviation on the Independent Variable concerned.
The largest Beta weight should have the greatest correlation with IQ. Look at the correlation table:-
Both English and IQ and French and IQ have significant correlations however, the partial correlations need to be observed to get the full picture.
Do we get the same results conducting a stepwise Multiple Regression on the same set of data?
The procedure is the same as before, with the exception of choosing ‘Stepwise’ in the Method box while in the Linear Regression Box rather than the default ‘Enter’.
Note the differences: Multiple Regression using the ‘Enter’ method enters all variables into the equation at the beginning. ‘Stepwise’ method only enters the variables which are good predictors into the final equation.
This time only English (previously recognised using the Enter method as the best predictor of IQ) is entered into the final equation and the Multiple Regression is significant.
As can be seen from the above table, English is a significant predictor of IQ, the other variables are excluded.
Differences in outcome are evident depending on the method selected. Sample size and number of variables need to be considered.
Though variables may correlate significantly, it fails to take into account partial correlations
Apply» Faculties & Departments» Department of Psychology» Labs» SPSS statistical procedures» Multiple Regression
