Question

An online clothing retailer examined their transactional database to see if total yearly Purchases (S) were related to customers' incomes (S). (Yo may assume that the assumptions and conditions for regression are ou met.) The least squares linear regression is shown below. Complete parts a through d. Purchases 32.8 +0.013(Income)

a) Interpret the intercept in the linear model.
A. The intercept of indicates the customer Income if the predicted total yearly Purchase was so.
B. The intercept of indicates the predicted total yearly Purchase if a customer's Income was $0
C. The intercept of is meaningless and should not be interpreted.
D. The intercept indicates that customer Income changes by for every $1 increase in total yearly Purchase.
b) Interpret the slope in the linear model. Select the correct choice below and fill in the answer box to complete your choice. A. The slope indicates that custome Income changes by s for every $1 increase in total yearly Purchase.
B. The slope of is meaningless and should not be interpreted
C. The slope indicates that the total yearly Purchase changes by s for every $1 increase in customer Income.
D. The slope of indicates the customer Income if he predicted total yearly Purchase was $0

Answer 1

(a) The correct option is (B).

(b) The correct option is (C).

Explanation:

The least squares linear regression for the total yearly Purchases related to customers' incomes is as follows:

`\text{Purchases} =32.8 +0.013\cdot \text{Income}`

Here,

Dependent variable = total yearly Purchases

Independent variable = customers' incomes

Intercept = 32.8

Slope = 0.013

(a)

An intercept of a least squares linear regression is the expected value of the dependent variable when the value of the independent variable is 0.

In this case the intercept is 32.8.

The intercept indicates that the total yearly Purchases of a customer with 0$ income is of worth $32.8.

Thus, the correct option is (B).

(b)

The slope of a least squares linear regression is the average rate of change in the dependent variable caused by 1 unit change in the independent variable.

In this case the slope is 0.013.

The slope indicates that with a $1 increase in incomes the total yearly Purchases of a customer increases by 0.013 units.

Thus, the correct option is (C).