Regression

Purpose:

Regression predicts or explains variability in a continuous outcome (DV) from one or more predictor variables (IVs). Simple linear regression uses one predictor; multiple regression uses two or more. In experimental designs with random assignment, regression can support causal inference — in correlational designs, it cannot.

Context Used:

  • ONE continuous DV
  • ONE or more continuous or categorical IVs (predictors)
  • A theoretical reason to predict the DV from the IV(s)
Do NOT use regression if: Your IV has only 2 groups and you just want to compare means → use a t-test | Your DV is categorical (yes/no, pass/fail) → use logistic regression | You have no theoretical reason to predict Y from X → use correlation instead | Assumptions below are violated

Assumptions:

  • Linearity: The relationship between each IV and the DV should be linear. Check with a residuals vs. fitted values plot — points should scatter randomly around zero with no curve.
  • Independence of residuals: Residuals should not be related to each other. Generally met by design in psychology research.
  • Homoscedasticity: The spread of residuals should be roughly equal across all predicted values. Look for a consistent band, not a funnel shape, in the residuals plot.
  • No multicollinearity (multiple regression only): IVs should not be excessively correlated with each other. Check "Collinearity statistics" in Jamovi — a VIF > 10 indicates a problem.
Check all four assumptions under "Assumption Checks" in Jamovi before interpreting output.

Jamovi Walkthrough:

  1. Click "Regression"
  2. Click "Linear Regression"
  3. Move the DV into the "Dependent Variable" box
  4. Move continuous IVs into "Covariates"; move categorical IVs into "Factors"
  5. Under "Model Fit," check "R²" and "F test"
  6. Under "Model Coefficients," check "Standardized estimate" and "Confidence interval"
  7. Under "Assumption Checks," check "Residuals plots" and "Collinearity statistics"

R Walkthrough:

model <- lm(outcome ~ predictor, data = df)
summary(model)
mcSummary(model)   # more detailed output

plot(model)   # 4 diagnostic plots

Output Interpretation:

R² (R-squared): The proportion of variance in the DV explained by the full model. Ranges from 0 to 1. Report as a percentage: "The model explained % of the variance in [DV]."

F-statistic and p-value:

  • If p < .05 → the overall model significantly predicts the DV.
  • If p > .05 → the model does not significantly predict the DV.

B (unstandardized coefficient): For every 1-unit increase in the IV, the DV changes by B units. Interpreted in the original units of measurement. The absolute size of B should be interpreted in context — do not assess it relative to 1.

β (standardized coefficient): B expressed in standard deviation units. Allows comparison of predictor importance across variables measured on different scales. A larger |β| means a stronger unique contribution to predicting the DV.

p-value (for each predictor):

  • If p < .05 → this predictor significantly predicts the DV.
  • If p > .05 → this predictor does not significantly predict the DV.

APA Format:

Appropriate data visualization: Scatterplot with regression line (simple regression). For multiple regression, use a regression table.

Sample write-up:

A simple linear regression examined whether [IV] predicted [DV]. The model was statistically significant, F(, ) = , p < .05, R² = . [IV] significantly predicted [DV], B = , β = , t() = , p = , 95% CI [, ].

Note: For multiple regression, report these statistics for each predictor in a regression table. Always report both B and β.

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