Is There a Relationship Between the Raises Administrators at State $( x )$

question 23

Multiple Choice

Is there a relationship between the raises administrators at State University receive and their performance on the job? A faculty group wants to determine whether job rating $( x )$ is a useful linear predictor of raise $( y )$ . Consequently, the group considered the straight-line regression model
$$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x .$$
Using the method of least squares, the faculty group obtained the following prediction equation:
$$\hat { y } = 14,000 - 2,000 x$$
Interpret the estimated slope of the line.

• A) For a \(\$ 1\) increase in an administrator's raise, we estimate the administrator's rating to decrease 2,000 points.
• B) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to decrease \(\$ 2,000\).
• C) For an administrator with a rating of 1.0, we estimate his/her raise to be \(\$ 2,000\).
• D) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase \(\$ 2,000\).

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Definitions:

Self-Fulfilling Prophecy

A belief or expectation that influences behaviors in a way that causes the belief to become a reality.

Projection

A defense mechanism where an individual ascribes their own unacceptable thoughts, feelings, or motives to another person.

Social Responsibility

The duty of individuals, organizations, or governments to act in a manner that benefits society at large, beyond their own interests.

Monitoring System

A tool or set of tools designed to track performance, activities, or conditions for the purpose of detecting changes or managing control.