Question

A study of 3535 ​secretaries' yearly salaries​ (in thousands of​ dollars) was done. The researchers want to predict salaries from several other variables. The variables considered to be potential predictors of salary are months of service left parenthesis x 1 right parenthesisx1​, years of education left parenthesis x 2 right parenthesisx2​, score on a standardized test left parenthesis x 3 right parenthesisx3​, words per minute​ (wpm) typing speed left parenthesis x 4 right parenthesisx4​, and ability to take dictation in words per minute left parenthesis x 5 right parenthesisx5. A multiple regression model with all five variables was run.	Variable	Coef	Std. Error	​t-value
	Intercept	9.7139.713	0.3730.373	26.04026.040
	x 1	0.1190.119	0.0140.014	8.5008.500
	x 2	0.0670.067	0.0210.021	3.1903.190
	x 3	0.0930.093	0.0390.039	2.3852.385
	x 4	0.0120.012	0.3160.316	0.0380.038
	x 5	0.0650.065	0.0230.023	2.8262.826

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

​a) What is the regression​ equation?

ModifyingAbove y with caretyequals=nothingplus+nothingx 1x1plus+nothingx 2x2plus+nothingx 3x3plus+nothingx 4x4plus+nothingx 5x5

​(Use integers or decimals for any numbers in the​ expression.)

​b) From this​ model, what is the predicted salary

ModifyingAbove y with carety

​(in thousands of​ dollars) of a secretary with

66

years

​(7272

​months) of​ experience,

99th

grade education

​(99

years of​ education), a

4747

on the standardized​ test,

5858

wpm typing​ speed, and the ability to take

2929

wpm​ dictation?The predicted salary is

nothing

thousand dollars.

​(Round to one decimal place as​ needed.)

​c) Test whether the coefficient of words per minute of typing speed

left parenthesis x 4 right parenthesisx4

is significantly different from zero at

alphaαequals=0.050.05.

State the hypotheses.

A.

Upper H 0H0​:

Typing speed makes a useful contribution to the​ model,

beta 4β4equals=0

Upper H Subscript Upper AHA​:

Typing speed contributes nothing useful after allowing for the other predictors in the​ model,

beta 4β4not equals≠0

B.

Upper H 0H0​:

Typing speed makes a useful contribution to the​ model,

beta 4β4not equals≠0

Upper H Subscript Upper AHA​:

Typing speed contributes nothing useful after allowing for the other predictors in the​ model,

beta 4β4equals=0

C.

Upper H 0H0​:

Typing speed contributes nothing useful after allowing for the other predictors in the​ model,

beta 4β4not equals≠0

Upper H Subscript Upper AHA​:

Typing speed makes a useful contribution to the​ model,

beta 4β4equals=0

D.

Upper H 0H0​:

Typing speed contributes nothing useful after allowing for the other predictors in the​ model,

beta 4β4equals=0

Upper H Subscript Upper AHA​:

Typing speed makes a useful contribution to the​ model,

beta 4β4not equals≠0

Identify the test statistic.

nothing

Identify the critical​ value(s). Recall that

alphaαequals=0.050.05.

nothing

​(Use a comma to separate answers as needed. Round to three decimal places as​ needed.)

Test the null hypothesis​ (at

alphaαequals=0.050.05​)

and state your conlusion.

A.

RejectReject

the null hypothesis. The coefficient

isis

significantly different from zero.

B.

Fail to rejectFail to reject

the null hypothesis. The coefficient

isis

significantly different from zero.

C.

Fail to rejectFail to reject

the null hypothesis. The coefficient

is notis not

significantly different from zero.

D.

RejectReject

the null hypothesis. The coefficient

is notis not

significantly different from zero.

​d) How might this model be​ improved? Select all that apply.

A.Remove

x 4x4

from the regression equation.

B.Remove

x 5x5

from the regression equation.

C.Remove

x 3x3

from the regression equation.

D.Remove

x 1x1

from the regression equation.

E.Remove

x 2x2

from the regression equation.​e) A correlation of age with salary finds r​ =

0.6890.689​,

and the scatterplot shows a moderately strong positive linear association.​ However, if

x 6x6equals=Age

is added to the multiple​ regression, the estimated coefficient of age turns out to be

negative 0.149−0.149.

Explain some possible causes for this apparent change of direction in the relationship between age and salary.

A.

Older secretaries tend of have fewer years of eduation.

B.

Older secretaries tend to have lower standardized test scores.

C.

Age is an insignificant factor in the model.

D.

Age is likely to be collinear with several of the other predictors already in the model.

Click to select your answer(s).

Answer 1