Final answer:
The prediction comparison between linear and logistic models for loan approval probability depends on the down payment and income-to-loan ratio. Logistic models are more suited to probabilities with an upper bound like loan approvals, while linear models predict a continuous increase or decrease without a bound.
Step-by-step explanation:
The question asks to compare the predictions of loan approval probability between a linear model and a logistic model for an applicant with different down payment percentages and a set income-to-loan ratio. In general, a linear model will continuously increase or decrease the probability of loan approval as the down payment increases, without bound. However, a logistic model, which is often used for binary outcomes such as loan approval or denial, will show an S-shaped curve where the probability of approval approaches 1 (or 100%) as the down payment increases, but will never actually reach or exceed 100%.
As for the question of which model predicts better, it depends on the nature of the data and the expected outcome. If the probability of loan approval does not simply increase indefinitely as the down payment increases but tends to taper off, forming a threshold after which more down payment has minimal additional effect, then the logistic model would perform better. Conversely, if the probability of approval continues to increase without plateauing, the linear model might be preferred, even though in reality, such an unbounded increase is unlikely in loan approval scenarios.