You have run your regression in SPSS or R. Now you are looking at a table full of numbers — coefficients, standard errors, t-values, p-values, R², and things labelled VIF — and your dissertation deadline is tomorrow. This guide explains each element in plain English.
The Model Summary: R² and Adjusted R²
R² (R-squared) tells you how much of the variation in your dependent variable is explained by your independent variables. An R² of 0.63 means your model explains 63% of the variation in the outcome. In social science and business research, R² values of 0.25–0.65 are common and acceptable — you don't need R² = 0.90 to have a meaningful model.
Use Adjusted R² when you have multiple independent variables. It penalises for adding variables that don't actually improve the model, giving a more honest picture of fit.
The ANOVA Table: Is the Model Significant?
Before examining individual coefficients, check whether the overall model is statistically significant. In the ANOVA table, look at the F-statistic and its Sig. (significance) value. If Sig. < 0.05, your model as a whole is statistically significant — the combination of predictors explains the outcome better than chance.
Coefficients: Understanding Each Predictor
The coefficients table shows, for each independent variable: the unstandardised coefficient (B), standard error, standardised coefficient (Beta), t-statistic, and significance level (Sig.).
- B (unstandardised coefficient): For every one-unit increase in X, Y changes by B units — holding all other variables constant.
- Beta (standardised coefficient): Allows you to compare the relative importance of different predictors (all on the same scale). Higher absolute Beta = stronger predictor.
- Sig. (p-value): If Sig. < 0.05, the predictor is statistically significant. If Sig. > 0.05, that predictor may not have a meaningful relationship with the outcome in your sample.
Checking Assumptions
Multicollinearity (VIF): Check the Collinearity Statistics column. VIF values above 10 (some say 5) suggest multicollinearity — your predictors are too highly correlated with each other, making individual coefficient interpretation unreliable. Consider removing one of the correlated predictors.
Residual Normality: Check the P-P Plot or histogram of residuals. Residuals should be approximately normally distributed. A curved P-P plot suggests non-normality — note this as a limitation.
Homoscedasticity: Check the scatterplot of standardised residuals against predicted values. Points should be randomly distributed — a funnel shape indicates heteroscedasticity, which can affect the reliability of significance tests.
Reporting Regression in Your Dissertation
Report as: "A multiple linear regression was conducted to predict [Y] from [X1, X2, X3]. The model was statistically significant, F(df1, df2) = [F-value], p < .001, and explained [R²]% of variance in [Y] (Adjusted R² = [value]). [X1] was the strongest predictor (β = [Beta], p = [Sig.]), followed by [X2] (β = [Beta], p = [Sig.])."