Question

Bankers at a large financial institution created the linear regression model dˆ=0.37−0.0004s to predict the proportion of customers who would default on their loans, d , based on the customer’s credit score, s . For a customer with a credit score of 700, which of the following is true?

Answer 1

The correct option is (a).

Explanation:

The complete question is:

Bankers at a large financial institution created the linear regression model dˆ=0.37−0.0004s to predict the proportion of customers who would default on their loans, d , based on the customer’s credit score, s . For a customer with a credit score of 700, which of the following is true?

(a) The default proportion is predicted to be 0.09.

(b) The default proportion will be 0.09.

(c) The default proportion is predicted to be approximately 1.75 million.

(d) The default proportion will be approximately 1.75 million.

(e) The default proportion is predicted to be 0.28.

Solution:

The linear regression model is used to predict the value of the response or dependent variable based on only one explanatory or independent variable.

The general form of a linear regression model is:

`\hat y=\alpha +\beta x`

Here,

y = dependent variable

x = independent variable

α = intercept

β = slope

The linear regression model to predict the proportion of customers who would default on their loans, based on the customer’s credit score is:

`\hat d=0.37-0.0004\ s`

d = default on loans

s = customer’s credit score

Compute the predicted value of d for s = 700 as follows:

`\hat d=0.37-0.0004\ s`

`=0.37-(0.0004* 700)\\=0.37-0.28\\=0.09`

Thus, for a customer with a credit score of 700, the default proportion is predicted to be 0.09.

Thus, the correct option is (a).