# Question

The AFL-CIO has undertaken a study of 30 secretaries’ yearly salaries (in thousands of dollars). The organization wants to predict salaries from several other variables. The variables to be considered potential predictors of salary are:

X1 = months of service

X2 = years of education

X3 = score on standardized test

X4 = words per minute (wpm) typing speed

X5 = ability to take dictation in words per minute

A multiple regression model with all five variables was run on a computer package, resulting in the following output.

Assume that the residual plots show no violations of the conditions for using a linear regression model.

a) What is the regression equation?

b) From this model, what is the predicted salary (in thousands of dollars) of a secretary with 10 years (120 months) of experience, 9th grade education (9 years of education), 50 on the standardized test, 60 wpm typing speed, and the ability to take 30 wpm dictation?

c) Test whether the coefficient for words per minute of typing speed (X4) is significantly different from zero at α = 0.05.

d) How might this model be improved?

e) A correlation of age with salary finds r = 0.682 and the scatterplot shows a moderately strong positive linear association. However, if X6 = Age is added to the multiple regression, the estimated coefficient of age turns out to be b6 = -0.154. Explain some possible causes for this apparent change of direction in the relationship between age and salary.

X1 = months of service

X2 = years of education

X3 = score on standardized test

X4 = words per minute (wpm) typing speed

X5 = ability to take dictation in words per minute

A multiple regression model with all five variables was run on a computer package, resulting in the following output.

Assume that the residual plots show no violations of the conditions for using a linear regression model.

a) What is the regression equation?

b) From this model, what is the predicted salary (in thousands of dollars) of a secretary with 10 years (120 months) of experience, 9th grade education (9 years of education), 50 on the standardized test, 60 wpm typing speed, and the ability to take 30 wpm dictation?

c) Test whether the coefficient for words per minute of typing speed (X4) is significantly different from zero at α = 0.05.

d) How might this model be improved?

e) A correlation of age with salary finds r = 0.682 and the scatterplot shows a moderately strong positive linear association. However, if X6 = Age is added to the multiple regression, the estimated coefficient of age turns out to be b6 = -0.154. Explain some possible causes for this apparent change of direction in the relationship between age and salary.

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