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:

Labeling Theorists

Social scientists who study how the labels or names applied to individuals by society can influence perceptions and behaviors, often as part of the broader study of deviance and social control.

Deviance

Actions or behaviors that breach the norms or expectations set by society.

Violation

The act of breaking or failing to comply with a rule, agreement, or law.

Social Rule

Guidelines and norms that govern behavior within a society or group, often implied and learned through social interaction.