Find the Least-Squares Regression Line and Use the Line to Make

question 153

Multiple Choice

Find the Least-Squares Regression Line and Use the Line to Make Predictions
-A manager wishes to determine the relationship between the number of years her sales representatives have been employed by the firm and their amount of sales (in thousands of dollars) per month. Find the equation of the regression line for the given data. What would be the predicted sales if the sales representative was employed by the firm for 30 years Is this reasonable? Why or why not?
$\begin{array}{|l|c|c|c|c|c|c|c|c|c|}\hline \text { Years employed, x } & 2 & 3 & 10 & 7 & 8 & 15 & 3 & 1 & 11 \\\hline \text { Sales, y } & 31 & 33 & 78 & 62 & 65 & 61 & 48 & 55 & 120\end{array}$

• A) \(\hat { y } = 3.53 \mathrm { x } + 37.92 ; \$ 143,820\); No; it is not reasonable. 30 years of employment is well outside the scope of the model.
• B) \(\hat { y } = 3.53 x + 37.92 ; \$ 143,820 ;\) Yes, it is reasonable.
• C) \(\hat { y } = 3.53 \mathrm { x } - 37.92 ; \$ 67,980 ; \mathrm { No }\); it is not reasonable. 30 years of employment is well outside the scope of the model.
• D) \(\hat { y } = 3.53 \mathrm { x } - 37.92 ; \$ 67,980\); Yes; it is reasonable.

---

Definitions:

Informal Group

A group formed naturally within an organization based on personal relationships or shared interests rather than organizational structure.

Groupthink

A mental effect found in a group setting where the preference for unity or agreement leads to illogical or ineffective choices.

Cohesiveness

The measure of the bond or strength of the relationships uniting the members of a group or team towards a common objective.

Pay Equity

The concept of ensuring equal pay for work of equal value, aimed at eliminating gender and other discriminatory pay gaps.