Question

Is there a relationship between a person's height and the salary he or she earns? In a study published in the Journal of Applied Psychology,† a positive correlation was found between the heights and the salaries of the participants. The correlation was found to be strongest for employees in sales and management positions. Suppose you conduct a similar study by obtaining height and earnings data from 20 randomly selected people in your community.

You use statistical computing software (such as Excel) to compute the following regression equation predicting salary (in $1,000 units) from height (in inches): salary = 32.1 + 0.109 height (a)

QUESTION A- Using this regression equation, you would predict that someone 5'5" (65 inches) tall earns $ .

QUESTION B- You meet friends who live in your community for lunch. One friend tells you she is 5'3" (63 inches) tall and makes $32,655. What does this information tell you about the regression equation you derived using your sample?

The regression equation was calculated incorrectly, because it would predict your friend earns $38,967.

Your friend must not be part of the sample used to derive the equation, or else the amount she earns would be $38,967.

Nothing. The predicted average amount a person who is 5'3" is $38,967, but this does not mean this will be precisely true for any person who is 5'3" tall in the population.

The sample you selected must not be representative of the population, because your friend is part of the population and earns less than would be predicted by the regression equation.

QUESTION C- The people in your sample range in height from 4'10" (58 inches) to 6'1" (73 inches). Another friend at lunch is currently looking for a job and asks you if you can use your equation to predict how much he will earn. He is 6'10" (82 inches) tall. Which of the following is the most appropriate response?

The regression equation predicts that he will earn $41,038.

Since his height is far outside of the range of the data used to derive the equation, the regression equation shouldn't be used to make a prediction.

The regression equation predicts that he will earn $53,338.

Answer 1

You use statistical computing software (such as Excel) to compute the following regression equation predicting salary (in $1,000 units) from height (in inches): salary = 32.1 + 0.109 height (a)

QUESTION A- Using this regression equation, you would predict that someone 5'5" (65 inches) tall earns $ .

= 32.1 + 0.109 * 65

= 39.185( as units in 1000)

=$39185

----------------------------------------

QUESTION B- You meet friends who live in your community for lunch. One friend tells you she is 5'3" (63 inches) tall and makes $32,655. What does this information tell you about the regression equation you derived using your sample?

The sample you selected must not be representative of the population, because your friend is part of the population and earns less than would be predicted by the regression equation.

------------------------------------

QUESTION C- The people in your sample range in height from 4'10" (58 inches) to 6'1" (73 inches). Another friend at lunch is currently looking for a job and asks you if you can use your equation to predict how much he will earn. He is 6'10" (82 inches) tall. Which of the following is the most appropriate response?

Since his height is far outside of the range of the data used to derive the equation, the regression equation shouldn't be used to make a prediction.

Please revert in case of any doubt.

Please upvote. Thanks in advance