Question 12: A bank wants to predict whether a customer will default …

A bank wants to predict whether a customer will default on a loan using a classification model. The bank collects data from past customers, which includes the following features:

• $x_1$: Credit score (scaled between 0 and 1)
• $x_2$: Monthly income (in $1000s)
• $x_3$: Number of late payments in the past year

The target variable $y$ represents whether the customer defaulted (1 for default, 0 for no default). The data is provided in the table below:

The bank uses the following linear combination to compute $z$:

$z = 0.5x_1 + 0.3x_2 - 0.2x_3$

The step function $u(z)$ is used to classify the outcome:

$u(z) = \begin{cases} 1 & \text{if } z \ge 1.5 \\ 0 & \text{otherwise} \end{cases}$

Based on the above data, answer the given subquestions.

If the threshold in the step function is changed to z ≥ 1.0, what will happen to the misclassification rate?