Business Context

LendWise is building a logistic regression model to predict 90-day loan default. Before modeling, the team wants to use correlation analysis to remove weak predictors and flag redundant features.

Problem Statement

You are given correlations between five candidate features and the binary target default_flag, plus pairwise correlations among the features. Use correlation analysis to decide which features should be kept, dropped, or reviewed further before fitting the model.

Given Data

Assume the team computed Pearson correlations on a training sample of 1,200 applicants.

Pairwise feature correlations:

Use a two-sided significance level of $\alpha = 0.05$. For screening, treat absolute correlation below 0.05 as operationally negligible, and treat pairwise feature correlation above 0.80 as a multicollinearity warning.

Requirements

1. Test whether annual_income and months_with_bank are significantly correlated with the target.
2. Compute the test statistic for each correlation using the sample size provided.
3. Decide which features would be dropped for weak target relationship.
4. Identify any pair of features that creates a redundancy concern.
5. Recommend a final feature set for an initial model and explain the trade-off.

Assumptions

• Correlations were computed on the same 1,200-row training sample.
• Use Pearson correlation as a first-pass screening tool.
• Correlation screening is not the final modeling step; domain judgment still matters.