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MASH : Maths and Stats Help

Multiple Linear Regression

Introduction

A Multiple Linear Regression is an expansion of a Simple Linear Regression allowing multiple predictors to be incorporated into a single model.

It is considered a parametric test and is only suitable for parametric data. To check if your data is parametric, please check out the dedicated guide: Parametric or Not Guide (PDF)

 

Test Procedure

  1. Click Analyze > Regression > Linear

  2. Within the 'Linear Regression' window, select your Outcome variable and move it to the 'Dependent' box, select your Predicitor variables and move to to the 'Block 1 of 1' box.

  3. Select Statistics and click Estimates, Confidence Intervals, Model Fit, R Squared Change, and Descriptives

  4. Click Continue, click OK

 

Results

SPSS will generate a large number of tables, for this test we need the final three, the Model Summary, the ANOVA and the Coefficients.

Model Summary

This table shows a selection of descriptive statistics about the model/regression overall: the R-value (R), the R-Squared Statistic (R Square), the F statistic measuring change (F Change) and the p-value associated with the F stat change (Sig. F Change)

ANOVA

This table shows a further  selection of descriptive statistics about the model/regression overall: two different Degrees of Freedom (df) , the F statistic measuring change (F Change) and the p-value associated with the F stat change (Sig. F Change)

Coefficients

This final table shows the exact values of the constant and all of our predictors, it also shows if the variables are significant (Sig.) and the 95% Confidence intervals (95.0% Confidence Interval for B)

Reporting the Results in APA Formatting

A multiple linear regression was used to predict a student's physics score using their mathematics and English scores. The models did explain a significant amount of the variance in the physics scores, F(2,168)= 20.72, p < .001, R2=.20. Mathematics score was a significant predictor of physics score (B=0.43, t(168) = 6.22, p<.001) with an increase of one point in mathematics score, would correspond, on average, an increase in physics score by 0.49 points 95% CI [0.34,0.66]. English score was not a significant predictor of physics score (B = -0.08, t(168) = -1.19, p = .234) with an increase of one point in mathematics score, would correspond, on average, to a decrease in physics score by -0.10 points 95% CI [-.26, 0.64].