Fit and interpret multiple linear regression models for marketing data with a mix of continuous and categorical predictors. Upload raw rows, pick your outcome, and compare the marginal effects of each predictor with confidence intervals and diagnostics.
Multiple linear regression estimates how an outcome \(Y\) changes, on average, with several predictors \(X_1, X_2, \dots, X_p\). Each coefficient shows the unique association of a predictor with the outcome, holding the others constant.
Model: $$ Y_i = \beta_0 + \beta_1 X_{1i} + \beta_2 X_{2i} + \dots + \beta_p X_{pi} + \varepsilon_i $$
Coefficient tests: $$ t = \frac{\hat{\beta}_j}{\mathrm{SE}(\hat{\beta}_j)}, \quad \nu = n - p - 1 $$
Overall model test: $$ F = \frac{(SSR/p)}{(SSE/(n - p - 1))} $$
Continuous predictors use their numeric scale. Categorical predictors are dummy-coded with a reference level, so each coefficient compares a category to its reference while holding other predictors constant.
Use presets to explore realistic use cases, such as ad spend vs. revenue or control vs. treatment on order value. Each scenario can expose either a summary CSV of aggregated statistics or a raw data file that you can download, edit in Excel, and re-upload.
Upload a CSV file with raw case-level data. Include one outcome variable and multiple predictors (numeric or categorical). Headers are required.
Drag & Drop raw data file (.csv, .tsv, .txt)
Include headers; at least one numeric outcome column and predictors (numeric or text for categorical).
No file uploaded.
Need a starter file? Use the raw template with 3 continuous and 2 categorical predictors (50 observations).
Set the significance level for hypothesis tests and confidence intervals.
Each point compares an observed outcome to its predicted value. Points near the 45-degree line indicate better fit. Curves or funnel shapes can signal non-linearity or changing variance; far-off points may be influential cases to review.
Continuous controls default to mean; categorical controls default to modal (most frequent) level.
| Variable | Mean | Median | Std. Dev. | Min | Max |
|---|---|---|---|---|---|
| Provide data to see summary statistics. | |||||
| Predictor | Level | Percent |
|---|---|---|
| Provide data to see level percentages. | ||
Provide data to see the fitted regression equation.
The downloaded file includes your original raw data plus two columns: y_fitted (the model’s
predicted value for each observation) and residual (actual minus predicted). These are useful for
custom diagnostics, plotting, or follow-up modeling outside the tool.
R-squared / Adj. R-squared: Percent of outcome variation explained by the predictors (adjusted version penalizes extra predictors). Marketing takeaway: higher means the model captures more of what drives the outcome.
Model F & p-value: Tests whether, as a set, the predictors improve prediction vs. no predictors. A small p-value (< alpha) means the model adds meaningful signal.
RMSE / MAE / Residual SE: Typical prediction error size. Smaller is better. RMSE/Residual SE put more weight on large misses; MAE is the average absolute miss.
DF (model/error) & n: Sample size and available information for estimating effects. Very low error DF can make estimates unstable.
Alpha: Your chosen significance level. P-values below alpha are treated as statistically reliable; above alpha are treated as not statistically reliable.
| Predictor | Level / Term | Estimate | Standard Error | t | p-value | Partial η2 | Lower Bound | Upper Bound |
|---|---|---|---|---|---|---|---|---|
| Provide data to see coefficient estimates. | ||||||||
Run the analysis to see checks on multicollinearity, variance patterns, and normality of residuals. Use these as prompts for plots and follow-up modeling, not as strict pass/fail gates.