Binary Logistic Regression with Minitab

Understand odds and probability, learn how odds are calculated from events and non-events, and see practical examples with coin flips and dice to inform simple binary logistic regression.

Derive odds from probability using the formula odds equals P over one minus P and see an example with American Express card ownership, where 4/7 probability yields 4/3 odds.

Explore natural log and exponential concepts, including base 10 and base e, their inverse relationship, and practical log properties used in logistic regression.

Explore how odds relate to probability, learn to compute log odds using the natural log, and see how the logit function underpins binary logistic regression in Minitab.

Derive the logistic regression probability using log odds and the equation P = exp(b0 + b1 x) / (1 + exp(b0 + b1 x)), with binary outcomes and Minitab outputs.

Perform logistic regression in Minitab to predict American Express card ownership from annual income using a logit model and a fitted line plot.

Explain how the logistic regression equation uses annual income to predict the probability of having an American Express card, using the logit function and Minitab predictions.

Explore how the odds ratio in binary logistic regression links a predictor such as annual income to probability changes via the logit and natural log of odds, with confidence intervals.

Explore how logistic regression in Minitab uses annual income to estimate probability and odds ratio, then interpret the anova p-value against alpha 0.05 to assess a relationship.

Explain type I and type II errors, alpha, and p-values in regression hypothesis testing, showing how a low p-value supports including income as a predictor.

Explore binary logistic regression with Minitab and learn to read the confusion matrix, area under the ROC curve, and model summary for annual income as a predictor and prediction accuracy.

Explore how to interpret a confusion matrix from Minitab, compute precision (sensitivity) and specificity, and plot the first ROC curve point to assess model performance.

Explore constructing an ROC curve from a confusion matrix, and adding extreme cut points to understand how thresholds affect sensitivity and specificity and the area under the ROC curve.

Shows how adjusting the cut point generates ROC curve points, updates the confusion matrix and metrics like precision, sensitivity, and specificity, and uses Minitab to plot the ROC and AUC.

Plot a ROC curve in Minitab 19 from a binary logistic regression using annual income to predict American Express, and examine the area under the curve of 0.8852.

Analyze how the ROC curve balances sensitivity and specificity, identify the random model via the 45-degree line, and interpret the area under the curve (AUC), here 0.8852.

Understand deviance r-square and its adjusted form for logistic model fit, note multiple pseudo r-squares (McFadden, Cox-Snell, Efron), and that Minitab provides only deviance r-square.

Calculate r-squared using the count method from a confusion matrix to measure model efficiency, then use adjusted count r-squared to correct bias in imbalanced outcomes.

examine deviance r-squared and the model summary criteria—aic, aicc, and bic—to compare models, with area under the roc curve as the priority and residual plots for validation.

Introduce the goodness-of-fit test for logistic regression by comparing deviance, Pearson, and Hosmer-Lemeshow p-values to a 0.05 alpha, and show that the model fits the data.

Explore how the Deviance and Pearson goodness-of-fit tests compare a logistic regression model to a saturated full model, and why the Hosmer-Lemeshow test, using observed versus expected frequencies, is preferred.

Compare the model to the saturated model using deviance and Pearson goodness-of-fit, noting the five-event-per-profile requirement; with continuous predictors, prefer the Hosmer-Lemeshow test for fit.

Learn how to perform the Hosmer Lemeshow Goodness of Fit Test in Minitab for binary logistic regression, interpreting observed versus expected frequencies, chi-square, and a p-value (0.976) indicating good fit.

Analyze logistic regression results using a three-in-one graph, including ROC curve and residual plots (normal probability, histogram, versus order) to assess normality, patterns, and model fit.

Explore how to prepare data for binary logistic regression in Minitab, including understanding income, children, and viewed ads, checking missing values, and using cross tabulations to assess buying behavior.

Explore how income, children, and ad view influence cereal purchases using individual value plots and stacked bar charts, laying the groundwork for binary logistic regression in Minitab.

Perform binary logistic regression on cereal purchase data using income, children, and viewed ad. Remove income improves the model, and interpret odds ratios and predicted probabilities for different factor combinations.

Use stepwise selection in Minitab to build a binary logistic regression model, removing income and keeping only children and view ad, with possible interactions considered.