Fit and interpret logistic regression models for marketing data with a binary outcome and a mix of continuous and categorical predictors. Upload raw rows, pick your success outcome, and compare the marginal effects of each predictor on conversion probabilities with confidence intervals and diagnostics.
Logistic regression estimates how the probability of a binary outcome (such as convert vs. not convert) changes with several predictors \(X_1, X_2, \dots, X_p\). Each coefficient shows the unique association of a predictor with the log-odds of success, holding the others constant.
Model: $$ \log\left(\frac{p_i}{1 - p_i}\right) = \beta_0 + \beta_1 X_{1i} + \beta_2 X_{2i} + \dots + \beta_p X_{pi} $$ where \(p_i = \Pr(Y_i = 1 \mid X_{1i}, \dots, X_{pi})\).
Coefficient tests: $$ z_j = \frac{\hat{\beta}_j}{\mathrm{SE}(\hat{\beta}_j)} $$ with p-values based on the standard normal distribution.
Model comparison: $$ \Delta D = D_{\text{null}} - D_{\text{model}} $$ can be compared using a chi-square test to see whether the predictors, as a set, improve fit vs. an intercept-only model.
The outcome must be coded as a binary variable (for example, 0/1 or success/failure). 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 binary outcome column (0/1 or two categories) and multiple predictors (numeric or categorical). Headers are required.
Drag & Drop raw data file (.csv, .tsv, .txt)
Include headers; at least one binary outcome column and predictors (numeric or text for categorical).
No file uploaded.
Set the significance level for hypothesis tests and confidence intervals.
Standardization affects model fitting and effect plots only. Summary statistics always report predictors on their original scale.
Each point plots a fitted probability on the horizontal axis and the observed 0/1 outcome (with a small amount of vertical jitter for visibility) on the vertical axis. Points clustered near 0 or 1 on the x-axis indicate confident predictions; a mix of 0s and 1s at similar fitted probabilities indicates uncertainty. Strong patterns or obvious outliers can signal model misspecification or influential cases to review.
Choose levels/values for the non-focal predictors used when plotting the focal curve.
The line (or bars for categorical focals) shows the predicted probability that the focal outcome (coded as 1) occurs while holding other predictors constant at chosen values. Steeper slopes or larger gaps between bars imply stronger effects. Confidence bands/bars reflect the statistical uncertainty for those probabilities; wider bands mean less certainty. If bands for different settings overlap heavily, the model may not distinguish them well at those values.
| 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: p_hat (the model’s
predicted probability of the focal outcome for each observation) and neg_loglik_contribution,
the individual contribution to the negative log-likelihood penalty used to fit the model.
Log-likelihood / Deviance: Log-likelihood measures how well the model explains the observed pattern of 0/1 outcomes; deviance is a scaled version that compares the fitted model to a saturated one. Lower deviance means better fit.
Model chi-square & p-value: Compares the fitted model to an intercept-only (null) model using the difference in deviance. A small p-value (< alpha) means the predictors, as a set, improve the ability to predict success vs. failure.
Pseudo R-squared: A rough analogue of R-squared that summarizes how much the model improves fit relative to the null model. It is useful as a descriptive measure but should not be overinterpreted as “percent of variance explained.”
n: Sample size and available information for estimating effects. Very small n can make estimates unstable or produce separation issues where a predictor perfectly predicts the outcome.
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 (log-odds) | Standard Error | z | p-value | Odds Ratio | 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.