# Statistics Resources

This guide contains all of the ASC's statistics resources. If you do not see a topic, suggest it through the suggestion box on the Statistics home page.

## Simple Linear Regression

The Simple Linear Regression is used to create a predictive model using one independent variable and one dependent variable. In a regression analysis, the independent variable may also be referred to as the predictor variable, while the dependent variable may be referred to as the criterion or outcome variable. The regression analysis builds on the simple correlational analysis, moving from a measure of relationship to one with predictive abilities.

Assumptions

1. Both variables are measured on a continuous scale (interval or ratio level of measurement)
2. There's a linear relationship between the variables - assessed using a scatterplot.
3. No significant outliers - can be identified on the scatterplot or using a box plot
4. Independence of observations - checked using Durbin-Watson statistic
5. Homoscedasticity - assessed through examination of a scatterplot of the residuals
6. Residuals are approximately normally distributed - checked using a histogram or P-P plots

Running Simple Linear Regression in SPSS

1. Analyze > Regression > Linear...
2. Place your independent variable in the "Independent(s)" box and the dependent variable in the "Dependent" box.
3. You can use the options in the "Statistics" and "Plots" options there to include outputs to check the assumptions of your test.
4. Click "OK" to generate the results.

Interpreting the Output

• Model Summary
• R = the simple correlation value
• R-Square = measure of effect size for the model - indicates how much of the variability in the dependent variable can be explained by the independent variable
• ANOVA
• used to interpret the significance of the overall model - follow decision rule guidelines
• test statistic = F-ratio
• associated probability = "Sig."
• Coefficients
• used to create the regression equation for the predictive model
• slope = Unstandardized Coefficient B value for predictor variable
• intercept = Unstandardized Coefficient B value for "(Constant)"
• identify which variables are significant predictors in the model
• test statistic = t
• associated probability = Sig.

Reporting Results in APA Style

A simple linear regression was calculated to predict job satisfaction from perceived appreciation. A significant regression equation was found (F(1,18) = 16.2132, p < .01) with an R2 of .516.