Dick Staples, another product manager with HeathCo (see Exercise 7), has mentioned to Barbara Lynch that he has found both the unemployment rate and the level of income to be useful predictors for some of the products under his responsibility.

a. Suppose that Ms. Lynch provides you with the following unemployment data for the northern region she is concerned with:

b. Plot a scattergram of SALES versus northern-region unemployment rate (NRUR). Does there appear to be a relationship? Explain.

c. Prepare a bivariate regression model of sales as a function of NRUR in the following form:

SALES = α + b (NRUR)

Write your answer in the following equation:

SALES = ________ +/- ________ (NRUR)

(Circle + or €“ as appropriate)

Write a memo to Ms. Lynch in which you evaluate these results and indicate how well you think this model would work in forecasting her sales series. Use the model to make a forecast of sales for each quarter of 2008, given the forecast for unemployment (FNRUR) that HeathCo has purchased from a macroeconomic consulting firm (MacroCast):

f. For the actual sales given in Exercise 7(e), calculate the root-mean-squared error for this model. How does it compare with what you found in Exercise 7(e)?

g. Barbara Lynch also has data on income (INC), in billions of dollars, for the region as follows:

Plot a scattergram of SALES with INC. Does there appear to be a relationship? Explain.

h. Prepare a bivariate regression model of SALES as a function of income (INC) and write your results in the equation:

SALES = α + b (INC)

SALES = _______ +/- _______ (INC)

(Circle + or €“ as appropriate)

Write a memo to Ms. Lynch in which you explain and evaluate this model, indicating how well you think it would work in forecasting sales.

HeathCo has also purchased a forecast of income from MacroCast. Use the following income forecast (INCF) to make your own forecast of SALES for 2008:

k. On the basis of the actual sales given in Exercise 7(e), calculate the root-mean-squared error for this model. How does it compare with the other two models you have used to forecast sales?

l. Prepare a time-series plot with actual sales for 1998Q1 through 2007Q4 along with the sales forecast you found in part (/') of this exercise. To accompany this plot, write a brief memo to Ms. Lynch in which you comment on the strengths and weaknesses of the forecasting model.

Unemployment Rate (%) 2nd 3rd 4th 1st Year Quarter Quarter Quarter Quarter 1998 8.4% 8.2% 8.4% 8.4% 1999 7.7 8.1 7.5 7.2 2000 6.9 6.3 6.5 6.5 6.3 6.4 2001 6.2 6.5 2002 6.8 7.9 8.3 8.0 10.7 8.0 2003 2004 8.0 9.6 8.0 10.2 8.9 11.5 2005 11.2 11.0 8.0 10.1 9.2 2006 8.5 8.0 7.9 2007 7.9 7.9 7.8 7.6