Question

Use this scenario for the next few questions.

An automotive workers union, in conjunction with top management, is negotiating a new hourly pay policy for union workers based on three variables: (1) job class, (2) years with the company, and (3) years as a union member at any company. The goal is to develop an equitable model that can objectively specify hourly pay, thereby reducing pay disparity grievances. Fifty union workers have been sampled and will be used as the basis for the pay model.

> fit<-lm(Hourly.Pay~factor(Job.Class)+Years.with.Company+Years.in.Union)
> summary(fit)

Call:
lm(formula = Hourly.Pay ~ factor(Job.Class) + Years.with.Company +
Years.in.Union)

Residuals:
Min 1Q Median 3Q Max
-3.2121 -0.3575 0.0000 0.5132 3.2121

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 11.8484 3.0862 3.839 0.001448 **
factor(Job.Class)25 5.0073 4.4026 1.137 0.272134
factor(Job.Class)27 2.9837 3.1952 0.934 0.364275
factor(Job.Class)29 5.2239 3.6399 1.435 0.170493
factor(Job.Class)31 7.1375 3.5644 2.002 0.062486 .
factor(Job.Class)32 4.7477 3.6688 1.294 0.214001
factor(Job.Class)34 6.4437 3.2117 2.006 0.062031 .
factor(Job.Class)36 5.3331 3.1182 1.710 0.106530
factor(Job.Class)37 1.4798 3.6253 0.408 0.688546
factor(Job.Class)39 7.0117 3.3152 2.115 0.050474 .
factor(Job.Class)40 5.2258 2.8701 1.821 0.087394 .
factor(Job.Class)41 10.0317 3.6429 2.754 0.014124 *
factor(Job.Class)42 11.9797 3.8069 3.147 0.006237 **
factor(Job.Class)43 14.6596 3.9229 3.737 0.001797 **
factor(Job.Class)44 14.3917 3.7661 3.821 0.001503 **
factor(Job.Class)45 7.5033 4.5170 1.661 0.116153
factor(Job.Class)47 7.1818 3.1027 2.315 0.034239 *
factor(Job.Class)48 11.0838 3.6444 3.041 0.007778 **
factor(Job.Class)49 12.7832 4.3891 2.912 0.010174 *
factor(Job.Class)51 3.4720 3.7196 0.933 0.364471
factor(Job.Class)52 6.9818 3.1845 2.192 0.043483 *
factor(Job.Class)53 12.0704 3.0345 3.978 0.001082 **
factor(Job.Class)54 12.9877 3.7772 3.438 0.003375 **
factor(Job.Class)55 8.8079 3.6026 2.445 0.026442 *
factor(Job.Class)56 7.5919 3.3146 2.290 0.035914 *
factor(Job.Class)57 9.6317 3.6429 2.644 0.017686 *
factor(Job.Class)59 9.6597 3.4047 2.837 0.011893 *
factor(Job.Class)60 13.3238 3.6460 3.654 0.002139 **
factor(Job.Class)61 15.0278 3.6431 4.125 0.000794 ***
factor(Job.Class)63 13.5719 3.0793 4.407 0.000440 ***
factor(Job.Class)66 11.5636 4.0025 2.889 0.010680 *
factor(Job.Class)73 13.8818 3.1845 4.359 0.000487 ***
Years.with.Company 0.6759 0.3333 2.028 0.059563 .
Years.in.Union -0.5799 0.3422 -1.695 0.109476
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.477 on 16 degrees of freedom
Multiple R-squared: 0.8845, Adjusted R-squared: 0.6463
F-statistic: 3.713 on 33 and 16 DF, p-value: 0.003628

> vif(fit)
GVIF Df GVIF^(1/(2*Df))
factor(Job.Class) 18.26627 31 1.047971
Years.with.Company 52.07035 1 7.215979
Years.in.Union 52.86273 1 7.270676

1.

What is the response variable?

Group of answer choices

hourly pay

job class

years with company

years with union

2.

What is the alternative hypothesis for the F-test?

Group of answer choices

hourly pay is important

none of job class, years with company, and years with union are important to the model

at least one of job class, years with company, and years with union are all important to the model

job class, years with company, and years with union are all important to the model

3.

What is the correct interpretation of the coefficient for job class 25?

Group of answer choices

After accounting for years with the company and years in the union, those in job class 25 make $5.00 less on average than the baseline job category

After accounting for years with the company and years in the union, those in job class 25 make $5.00 more on average than the baseline job category

For each increase in job class, an employee makes $5.00 more per hour.

4.

The VIF for Years in the Union is 52.86273. This means

Group of answer choices

predictions of hourly pay will vary greatly

Years in the Union is not correlated with the other predictor variables

Years in the Union is correlated with the other precitor variables

Years in the Union is correlated with hourly pay

5.

If using a regression model for prediction, it is important to

Group of answer choices

reduce R-squared

avoid collinearity

reduce standard error

6.

When adding a predictor to a regression model, adjusted R-squared

Group of answer choices

can decrease

always increases

stays the same or increases

Answer 1

1.

What is the response variable?

hourly pay

2.What is the alternative hypothesis for the F-test?

at least one of job class, years with company, and years with union are all important to the model

3.

What is the correct interpretation of the coefficient for job class 25?

For each increase in job class, an employee makes $5.00 more per hour.

4.

The VIF for Years in the Union is 52.86273. This means

Years in the Union is correlated with the other precitor variables

5.

If using a regression model for prediction, it is important to

avoid collinearity

reduce standard error

6.When adding a predictor to a regression model, adjusted R-squared

can decrease

always increases