Linear regression
Predict a numeric outcome from one or more columns, including stepwise entry.
When to use it
Use linear regression when you want an equation: how many exam points go with one extra study hour, holding anxiety constant? Correlation only says the columns move together. Regression gives the slope.
Assumptions
The outcome is numeric. The straight-line model is a fair summary, the spread of residuals is roughly even, and the rows are independent. Residual plots and collinearity diagnostics are how Tensr shows those checks. They are not a formal hypothesis test of the assumptions.
Running it in Tensr
Options
Prop
Type
cluster_by, scales, reference_levels, and derive_mean_log_rt are accepted for advanced and agent runs. They are not the main dialog.
Reading the output
Exam score predicted from hours and anxiety. Both slopes were built to be moderate. A noise column, practice, is not in this model.
| Term | Estimate | p-value | 95% CI low | 95% CI high |
|---|---|---|---|---|
| Intercept | 71.518 | < .001 | 63.003 | 80.034 |
| hours | 2.062 | .001 | 0.832 | 3.292 |
| anxiety | -2.092 | < .001 | -3.162 | -1.021 |
| Metric | Value |
|---|---|
| RMSE | 7.246 |
| Durbin-Watson | 1.929 |
| Jarque-Bera statistic | 0.394 |
| Jarque-Bera p-value | .821 |
| Residual skewness | 0.09 |
| Residual kurtosis | 2.743 |
OLS regression (enter) predicting score from 2 predictor(s), n = 96. Inferential test: t. The primary result is significant (p = < .001). This is large enough, in this sample, to treat the comparison this page is about as a real association rather than noise. Metrics: R² = 0.231; Adj. R² = 0.215; Observations = 96; F p-value = < .001.
Reporting (APA 7)
Stepwise regression
The same scores with method set to stepwise. Hours and anxiety are the two candidates.
| Step | Variable entered/removed | R² | ΔR² | F change | p |
|---|---|---|---|---|---|
| 1 | entered: anxiety | 0.14 | 0.14 | 15.268 | < .001 |
| 2 | entered: hours | 0.231 | 0.092 | 11.083 | .001 |
OLS regression (stepwise) predicting score from 2 predictor(s), n = 96. Inferential test: t.
OLS regression (enter) predicting score from 2 predictor(s), n = 96. Inferential test: t. This result is significant (p = < .001). The effect is moderate, so report its size with the p-value.
Coming from SPSS
Analyze → Regression → Linear.
SPSS Method offers Enter, Stepwise, Remove, Backward, and Forward. Tensr’s method values are enter, stepwise, backward, and forward. SPSS Statistics also offers collinearity and plots from the same dialog. Tensr’s switches are collinearity_diagnostics and residual_plots.
Related
Associations without slopes are bivariate correlation. Adding predictors in blocks you choose is hierarchical regression. A product term is moderation.