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The multiple regression analysis expands the simple linear regression to allow for multiple independent (predictor) variables. The model created now includes two or more predictor variables, but still contains a single dependent (criterion) variable.

**Assumptions**

- Dependent variable is continuous (interval or ratio)
- Independent variables are continuous (interval or ratio) or categorical (nominal or ordinal)
- Independence of observations - assessed using Durbin-Waston statistic
- Linear relationship between the dependent variable and
*each*independent variable - visual exam of scatterplots - Homoscedasticity - assessed through a visual examination of a scatterplot of the residuals
- No multicollinearity (high correlation between independent variables) - inspection of correlation values and tolerance values
- No outliers or highly influential points - outliers can be detected using casewise diagnostics and studentized deleted residuals
- Residuals are approximately normally distributed - checked using histogram, P-P Plot, or Q-Q Plot of residuals.

**Running Multiple Linear Regression in SPSS**

- Analyze > Regression > Linear...
- Place all independent variables in the "Independent(s)" box and the dependent variable in the "Dependent" box
- Click on the "Statistics" button to select options for testing assumptions. Click "Continue" to go back to main box.
- Click "OK" to generate the results.

**Interpreting Output**

- Model Summary
- R = multiple correlation coefficient
- R-Square = coefficient of determination - measure of variance accounted for by the model
- Adjusted R-Square = measure of variance accounted for by the model adjusted for the number of independent variables in the model

- ANOVA
- F-ratio = measure of how effective the independent variables, collectively, are at predicting the dependent variable
- Sig. (associated probability) = provides the probability of obtaining the F-ratio by chance

- Coefficients
- Unstandardized B(eta) = measure of how much the dependent variable varies with changes in one independent variable is changed when all other variables are held constant = used to create the multiple regression equation for predicting the outcome variable.
- t and Sig. = used to determine the significance of each independent variable in the model

**Reporting Results in APA Style**

A multiple regression was run to predict job satisfaction from salary, years of experience, and perceived appreciation. This resulted in a significant model, *F*(3, 72) = 16.2132, *p* < .01, *R2* = .638. The individual predictors were examined further and indicated that salary (*t* = 9.21, *p* < .01) and perceived appreciation (*t* = 15.329, *p* < .001) were significant predictors but, years of experience was not (*t* = 1.16, *p* = .135).

- Last Updated: May 22, 2023 7:20 AM
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