Question

A manager in an advanced manufacturing facility is interested in studying job performance rating and uses a sample of 30 workers to estimate a model ; where

= a job performance rating score between 0 and 100

= work experience in years

d = (code = 1) if advanced manufacturing certified and (code = 0) if not certified

The regression results are shown below.

Analysis of Variance

Source          DF      SS      MS     F      P

Regression       2  3919.3  1959.6  6.85  0.010

Residual Error  12  3434.0   286.2

Total           14  7353.3

S = 16.9166   R-Sq = 53.3%   R-Sq(adj) = 45.5%

Predictor            Coef  SE Coef     T      P

Constant             29.28    12.77  2.29  0.041

Job Experience      5.222    1.702  3.07  0.010

Certification      22.135    8.852  2.50  0.028

a) Given the regression output above, write the regression equation.

b) What job performance rating score would you estimate for a worker with 10 years of work experience who is certified in advanced manufacturing?

c) By how much does the advanced manufacturing certification increase the typical job performance rating score?

d) Test at a .05 significance level whether the advanced manufacturing certification dummy variable is significant. For full credit, show hypothesis, test statistic, critical value rejection rule, p-value rejection rule, state decision and interpret.

e) Conduct a joint test of significance to see if any of the set of regression coefficients could be different from zero. Use the .05 significance level. For full credit, show hypothesis, test statistic, critical value rejection rule, p-value rejection rule, state decision and interpret.

Answer 1

a)

Job performance = 29.28 + 5.222*Job Experience + 22.135*Certification

Y^ = 29.28 + 5.222*X1 + 22.135*X2

b)

If Job Experience = 10, Certification = 1

Job performance = 29.28 + 5.222*10 + 22.135*1 = 103.635

c)

By 22.135 units advanced manufacturing certification increase the typical job performance rating score

d)

Hypothesis:

H0: β2 = 0

Ha: β2 not = 0

t stat = 2.50

Critical value = 2.1788

t stat > t critical, Reject H0

the advanced manufacturing certification P value = 0.028 < 0.05, So the advanced manufacturing certification dummy variable is significant

e)

Hypothesis:

H0: β1 = β2 = 0

Ha: at least one β is not = 0

Test:

F stat = 6.85

critical value = 3.89

F stat > F critical, Reject H0

P value = 0 < 0.05, Reject H0

Model is significant at 0.05 significance level