Sensitivity measures the proportion of actual positives correctly identified. To increase sensitivity (catch more true events), you must lower the probability cutoff. This makes it easier for an observation to be classified as an event, increasing true positives but also increasing false positives (which lowers specificity). The other options do not directly manipulate the classification threshold to trade specificity for sensitivity.

With a 5% event rate, a model that simply predicts ‘non-churn’ for everyone would be 95% accurate but useless. The default 0.5 probability cutoff is often too high for rare events. A lower cutoff (e.g., 0.1 or 0.2) is typically needed to meaningfully classify the rare class. While overfitting (C) is a risk, the primary issue described is the model’s failure to identify positives, which is a classification threshold problem, not necessarily a model structure problem.

SBC (and AIC) are information criteria that penalize model complexity. A lower SBC value indicates a better model when balancing goodness-of-fit with the number of parameters, which helps prevent overfitting and promotes better generalization to new data. R-Square always increases with more variables and does not account for overfitting. Adjusted R-Square is also useful, but SBC is a strong criterion for model selection with a focus on generalization.

A VIF greater than 10 is a common rule-of-thumb indicator of severe multicollinearity. It means that the variance of that variable’s coefficient estimate is inflated because the variable is highly correlated with other predictors in the model. This makes the coefficient estimate unstable and its standard error large, leading to unreliable p-values and difficult interpretation. The solution isn’t scaling (D) but rather investigating and potentially removing or combining correlated variables.

The Hosmer-Lemeshow test (triggered by LACKFIT) groups observations by their predicted probabilities (e.g., into deciles) and performs a chi-square test comparing the observed vs. expected number of events in each group. The null hypothesis (H0) is that there is no significant difference, meaning the model fits well. Option A is tested by the Global Null Hypothesis (Likelihood Ratio test). Option B describes a deviance test comparison. Option C is similar to A.

This is the key distinction. LASSO (Least Absolute Shrinkage and Selection Operator) is a regularization method that adds a penalty based on the absolute sum of coefficients (L1 penalty). This process shrinks coefficients and can force some to be exactly zero, effectively performing variable selection. Traditional stepwise selection (forward/backward) is a discrete process—a variable is either in the model with its OLS-estimated coefficient or out of the model entirely; it does not involve coefficient shrinkage.

A funnel shape in a residual plot is the classic sign of heteroscedasticity, which means the variance of the errors is not constant across all levels of the predicted value. This violates one of the key assumptions of ordinary least squares (OLS) regression. The correct remedy might involve transforming the response variable (e.g., log transformation) or using a modeling technique like weighted least squares.

The odds ratio is multiplicative. An OR of 2.5 for a continuous variable means that for a one-unit increase in the predictor (here, $1000), the odds of the event become 2.5 times the original odds (a 150% increase). It is crucial to distinguish between odds and probability (Options A and C incorrectly mention probability). Option B calculates the percentage change correctly ((2.5-1)*100% = 150%) but states it as the odds increase by 150%, which is less precise than the multiplicative interpretation in D.

A studentized residual with an absolute value > 2 or 3 indicates an outlier in the response (Y) direction. Leverage (hat value) measures an observation’s extremity in the predictor (X) space; a common rule is that leverage > 2p/n (where p is # parameters, n is # obs) is high. Here, 0.15 may or may not be high depending on p/n. However, the key is that for an observation to be highly influential (e.g., on coefficients), it usually needs to have BOTH high leverage AND be an outlier. This observation is an outlier (residual=3.2) but does not have exceptionally high leverage (0.15 is moderate), so it likely has less influence on the model fit than a high-leverage outlier would.

Sensitivity measures the proportion of actual positives correctly identified. To increase sensitivity (catch more true events), you must lower the probability cutoff. This makes it easier for an observation to be classified as an event, increasing true positives but also increasing false positives (which lowers specificity). The other options do not directly manipulate the classification threshold to trade specificity for sensitivity.0