# MASH : Maths and Stats Help

### Simple Linear Regression

#### Introduction

A 'Simple' Linear Regression is the next step on from a correlation and attempts to predict one variable (the Outcome Variable) using another variable (the Predictor Variable).

It is considered a parametric test and therefore 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 variable 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" then "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 our predictor, it also shows if the variable is significant (Sig.) and the 95% Confidence Interval (95.0% Confidence Interval for B)

## Reporting the Results in APA Formatting

A simple linear regression was used to predict a student's physics score using their mathematics score. Mathematics scores did explain a significant amount of the variance in the physics scores, (1,167)= 39.92, p < .001, R= .19, R2adjusted = .19. The regression coefficient (= 0.51, 95% CI [0.35,0.67]) indicated that an increase in one point mathematics score, would correspond, on average, to an increase in physics score by 0.51 points.