Question: 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.

The table shown below is data for 50 displaced workers. This data set is also on VLT (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.

(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?

(h) Develop your own model 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.

(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.

(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?