The cost of unemployment is a major issue both at the state and federal levels

2.The cost of unemployment is a major issue both at the state and federal levels.  What drives the cost is not only the number of unemployed but also the length of unemployment for each person.  The longer a person is unemployed, the higher the cost to governments and businesses.  To address the factors driving the length of unemployment for the manufacturing sector, data was collected on the number of weeks a person is unemployed due to a layoff along with a series of independent variables as shown below.   

 

Edu:The number of years of education. 

Married:An indicator of whether (Y) or not (N) a person is married.

Head:An indicator of whether (Y) or not (N) the person is the head of a household. 

Tenure:The number of years on the most recent job.

Manager:An indicator of whether (Y) or not (N) the person was in a management position. Sales:An indicator of whether (Y) or not (N) the person was in a sales occupation.  

Age:The current age (in years) of the individual worker

 

The table shown below is data for 50 displaced workers.  This data set is also on Canvass  (Exam folder) in Minitab format (LAYOFFS.MTW) so you don’t have to re-enter the data. 

 

(a) Develop an estimated regression model to predict length of unemployment using all of the variables.         

 

Regression Analysis: Weeks versus Age, Educ, ...

 

The regression equation is

Weeks = 22.9 + 1.51 Age - 0.613 Educ - 10.7 Married - 19.8 Head + 0.426 Tenure

- 26.7 Manager - 18.6 Sales

 

 

Predictor     Coef  SECoef      T      P

Constant     22.85    18.87   1.21  0.233

Age         1.5093   0.3040   4.96  0.000

Educ       -0.6133   0.9362  -0.66  0.516

Married    -10.743    6.012  -1.79  0.081

Head       -19.779    5.837  -3.39  0.002

Tenure      0.4265   0.4669   0.91  0.366

Manager    -26.742    8.326  -3.21  0.003

Sales      -18.561    6.281  -2.96  0.005

 

 

S = 16.3497   R-Sq = 59.1%   R-Sq(adj) = 52.3%

 

 

Analysis of Variance

 

Source          DF       SS      MS     F      P

Regression       7  16250.4  2321.5  8.68  0.000

Residual Error  42  11227.1   267.3

Total           49  27477.5

 

 

Source   DF  Seq SS

Age       1  9161.4

Educ      1    71.6

Married   1     7.0

Head      1  2064.6

Tenure    1   666.8

Manager   1  1944.4

Sales     1  2334.6

 

 

Unusual Observations

 

ObsAge  Weeks    Fit  SE Fit  Residual  St Resid

10  33.0  13.00  46.37    5.51    -33.37     -2.17R

24  23.0   7.00  38.47    5.81    -31.47     -2.06R

 

R denotes an observation with a large standardized residual.

 

 

 

(b) State the hypotheses one needs to test for significance of the model developed in part (a).

 

 

(c) Is the model developed in (a) significant at a 5% significance level?  Explain.   

 

 

(d) State and interpret the R2 value.  

 

 

(e) Conduct a residual analysis and comment on the results.

 

 

 

 

(f) Are all of the variables in the full model significant?  If not, which ones are not significant?  Explain.

 

 

(g) Is there any problem with multicollinearity?  Explain.  If so what should one do about it? 

 

 

Correlations: Age, Educ, Married, Head, Tenure, Manager, Sales 

 

             Age     Educ  Married     Head   Tenure  Manager

Educ       0.100

           0.490

 

Married   -0.209   -0.151

           0.145    0.296

 

Head       0.027   -0.156   -0.449

           0.854    0.280    0.001

 

Tenure     0.459    0.174   -0.057   -0.046

           0.001    0.228    0.692    0.750

 

Manager    0.097    0.160    0.073   -0.200   -0.113

           0.504    0.266    0.616    0.164    0.435

 

Sales      0.137    0.124   -0.148   -0.013    0.097   -0.156

           0.343    0.393    0.306    0.926    0.504    0.279

 

 

Cell Contents: Pearson correlation

               P-Value

 

 

 

(h) Develop your own model which you think is the most appropriate predictor of weeks of unemployment.   Explain the results and why you think this is the best model.

 

 

Regression Analysis: Weeks versus Age, Head, Manager, Sales 

 

The regression equation is

Weeks = - 0.07 + 1.73 Age - 15.1 Head - 28.7 Manager - 17.4 Sales

 

 

Predictor     Coef  SECoef      T      P

Constant    -0.069    9.843  -0.01  0.994

Age         1.7252   0.2651   6.51  0.000

Head       -15.086    5.121  -2.95  0.005

Manager    -28.672    8.117  -3.53  0.001

Sales      -17.421    6.236  -2.79  0.008

 

 

S = 16.5069   R-Sq = 55.4%   R-Sq(adj) = 51.4%

 

 

Analysis of Variance

 

Source          DF       SS      MS      F      P

Regression       4  15216.0  3804.0  13.96  0.000

Residual Error  45  12261.5   272.5

Total           49  27477.5

 

 

Source   DF  Seq SS

Age       1  9161.4

Head      1  1339.8

Manager   1  2588.1

Sales     1  2126.7

 

 

Unusual Observations

 

ObsAge  Weeks    Fit  SE Fit  Residual  St Resid

24  23.0   7.00  39.61    5.29    -32.61     -2.09R

39  62.0  80.00  89.47    9.36     -9.47     -0.70 X

 

R denotes an observation with a large standardized residual.

X denotes an observation whose X value gives it large leverage.

 

 

 

 

 

Correlations: Age, Head, Manager, Sales 

 

             Age     Head  Manager

Head       0.027

           0.854

 

Manager    0.097   -0.200

           0.504    0.164

 

Sales      0.137   -0.013   -0.156

           0.343    0.926    0.279

 

 

Cell Contents: Pearson correlation

               P-Value

 

 

 

(i) Using your best model, what would be the estimated length of unemployment a person with the following characteristics:  Age = 40; Education level = 16 years; Married; Head of household; Tenure = 18 years; Not a manager; Not in a sales occupation. 

 

Predicted Values for New Observations

 

New ObsFit  SE Fit      95% CI          95% PI

1  53.85    3.50  (46.81, 60.89)  (19.87, 87.84)

 

 

Values of Predictors for New Observations

 

New ObsAge  Head   Manager     Sales

1  40.0  1.00  0.000000  0.000000

 

 

 

 

(j) Develop and interpret a 95% confidence interval and prediction interval for the individual  described in part (i) above. 

 

 

 

 

(k) How might the results of your model be used to help both state and federal government deal with the length of unemployment problem?

 

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  • 2. The cost of unemployment is a major issue both at the state and federal levels. What drives the cost is not only the number of unemployed but also the length of …