Secretary performance The AFL-CIO has undertakena study of 30 secretaries’ yearly salaries (in thousands ofdollars). The organization wants to predict salaries fromseveral other variables.The variables considered to be potential predictors ofsalary areX1 = months of serviceX2 = years of educationX3 = score on standardized testX4 = words per minute (wpm) typing speedX5 = ability to take dictation in words per minuteA multiple regression model with all five variables was runon a computer package, resulting in the following output:Variable Coefficient Std. Error t-ValueIntercept 9.788 0.377 25.960X1 0.110 0.019 5.178X2 0.053 0.038 1.369X3 0.071 0.064 1.119X4 0.004 0.307 0.013X5 0.065 0.038 1.734s = 0.430 R2 = 0.863Assume that the residual plots show no violations of theconditions for using a linear regression model.a) What is the regression equation? b) From this model, what is the predicted Salary (in thou-sands of dollars) of a secretary with 10 years (120 months) of experience, 9th grade education (9 years of education), a50 on the standardized test, 60 wpm typing speed, and theability to take 30 wpm dictation?c) Test whether the coefficient for words per minute oftyping speed (X4) is significantly different from zeroat a = 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 lin-ear association. However, if X6 = Age is added to the multiple regression, the estimated coefficient of Ageturns out to be b6 = -0.154. Explain some possible causes for this apparent change of direction in the rela-tionship between age and salary.

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Secretary performance 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 considered to be 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:
Variable Coefficient Std. Error t-Value
Intercept 9.788 0.377 25.960
X1 0.110 0.019 5.178
X2 0.053 0.038 1.369
X3 0.071 0.064 1.119
X4 0.004 0.307 0.013
X5 0.065 0.038 1.734
s = 0.430 R2 = 0.863
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 thou-
sands of dollars) of a secretary with 10 years (120 months)

of experience, 9th grade education (9 years of education), a
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 a = 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 lin-
ear 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 rela-
tionship between age and salary.

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