Interpret the Slope and the Y-Intercept of the Least-Squares Regression $\hat { y } = \beta _ { 0 } + \beta _ { 1 } \mathrm { x }$

question 148

Multiple Choice

Interpret the Slope and the y-intercept of the Least-Squares Regression Line
-A large national bank charges local companies for using its services. A bank official reported the results of a regression analysis designed to predict the bank's charges (y) , measured in dollars per month, for services rendered to local companies. One independent variable used to predict service charge to a company is the company's sales revenue (x) , measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model, $\hat { y } = \beta _ { 0 } + \beta _ { 1 } \mathrm { x }$ . The results of the simple linear regression are provided below.
$$\hat { \mathrm { y } } = 2,700 + 20 \mathrm { x } , \mathrm { s } = 65,2 \text {-tailed p-value } = 0.064 \text { (for testing } \beta _ { 1 } \text { ) }$$
Interpret the estimate of $\beta _ { 0 }$ , the $y$ -intercept of the line.

• A) There is no practical interpretation since a sales revenue of \(\$ 0\) is a nonsensical value.
• B) All companies will be charged at least \(\$ 2,700\) by the bank.
• C) About \(95 \%\) of the observed service charges fall within \(\$ 2,700\) of the least squares line.
• D) For every \(\$ 1\) million increase in sales revenue, we expect a service charge to increase \(\$ 2,700\).

---

Definitions:

School-Age Child

A child attending elementary or primary school, typically between the ages of 5 and 12 years.

Monitor Screen

The display unit of a computer or other electronic device, used for viewing visual output.

MEDLINE

A comprehensive bibliographic database managed by the National Library of Medicine, offering references and abstracts on life sciences and biomedical topics.

World's Largest

A descriptor indicating the largest size or extent of something globally, often used in records or comparisons.