Consider now that you have been asked to prepare a forecast of wholesale furniture sales for the entire United States. You have been given the monthly time-series data in the accompanying table:

WFS is wholesale furniture sales in millions of dollars. It is not seasonally adjusted. PHS measures new private housing starts in thousands. UR is the unemployment rate as a percent. You believe that furniture sales are quite probably related to the general state of the economy and decide to test whether the unemployment rate affects furniture sales. You expect that as the unemployment rate rises (and the economy thus shows some sign of difficulty), furniture sales will decline.

a. Summarize the results of your bivariate regression by completing the following table:

b. After discussing the results at a staff meeting, someone suggests that you fit a multiple-regression model of the following form:

WFS = b0 + b1(UR) + b2(M1) + b3(M2) + 64(M4) + 65(M9) + b6(M10)

Where:

Ml = A dummy variable for January

M2 = A dummy variable for February

M4 = A dummy variable for April

M9 = A dummy variable for September

M10 = A dummy variable for October

Summarize the results in the following table:

€¢ Do the signs of the coefficients make sense?

€¢ Are the coefficients statistically significant at a 95 percent confidence level (one-tailed test)?

€¢ What percentage of the variation in WFS is explained by the model?

c. After a staff meeting where these results were presented, another analyst suggested that serial correlation can cause problems in such regression models. Interpret the Durbin-Watson statistic in part (b) and suggest what problems could result if serial correlation is a problem.

Add PHS lagged three months and time-squared (T2) to the model and again examine the results for serial correlation. Summarize the results:

Have the additional two variables affected the existence of serial correlation?

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Data for Exercise 8 WFS UR PHS WFS UR PHS 1990M1 1,226.00 1,287.00 1,473.00 1,383.00 1,208.00 1,344.00 1,161.00 1,221.00 1,367.00 1,380.00 1,310.00 1,302.00 1,344.00 1,362.00 1,694.00 1,611.00 1,648.00 1,722.00 1,488.00 1,776.00 1,839.00 2,017.00 1,920.00 1,778.00 1,683.00 1,829.00 2,012.00 2,033.00 2,305.00 2,007.00 1,941.00 2,027.00 1,922.00 2,173.00 2,097.00 1,687.00 1,679.00 1,696.00 1,826.00 1,985.00 2,051.00 2,027.00 2,107.00 2,138.00 2,089.00 2,399.00 2,143.00 2,070.00 8.60000 8.90000 9.00000 9.30000 843.00 6.70000 7.20000 7.10000 1,938.00 1,869.00 1,873.00 1,947.00 1,847.00 1,845.00 1,789.00 1,804.00 1,685.00 1,683.00 1,630.00 1,837.00 1,804.00 1,809.00 1,723.00 1,635.00 1,599.00 1,583.00 1,594.00 1,583.00 1,679.00 1,538.00 1,661.00 1,399.00 1,382.00 1,519.00 1,529.00 1,584.00 1,393.00 1,465.00 1,477.00 1,461.00 1,467.00 1,533.00 1,558.00 1,524.00 1,678.00 1,465.00 1,409.00 1,343.00 1,308.00 1,406.00 1,420.00 1,329.00 1,264.00 1,428.00 1,361.00 1994M1 1994M2 1994M3 1,866.00 1,843.00 2,001.00 2,165.00 2,211.00 2,321.00 2,210.00 2,253.00 2,561.00 2,619.00 2,118.00 2,169.00 2,063.00 2,032.00 2,349.00 2,218.00 2,159.00 2,240.00 2,335.00 2,388.00 2,865.00 2,829.00 2,432.00 2,395.00 1,995.00 2,232.00 2,355.00 2,188.00 2,177.00 2,333.00 2,124.00 2,463.00 2,435.00 2,688.00 2,604.00 2,393.00 2,171.00 2,136.00 2,428.00 2,264.00 2,402.00 2,320.00 2,258.00 2,675.00 2,676.00 2,629.00 2,610.00 1990M2 866.00 931.00 917.00 1,025.00 902.00 1990M3 1990M4 1994M4 7.20000 7.20000 7.20000 1990M5 9.40000 1994M5 1990M6 9.60000 1994M6 1990M7 1990M8 1990M9 9.80000 9.80000 10.1000 10.4000 1,166.00 1,046.00 1,144.00 1,173.00 1,372.00 1,303.00 1,586.00 1,699.00 1,606.00 1,472.00 1,776.00 1,733.00 1,785.00 1,910.00 1,710.00 1,715.00 1,785.00 1,688.00 1,897.00 2,260.00 1,663.00 1,851.00 1,774.00 1,843.00 1,732.00 1,586.00 1,698.00 1,590.00 1,689.00 1,612.00 1,711.00 1,632.00 1,800.00 1,821.00 1,680.00 1,676.00 1,684.00 1,743.00 1,676.00 1,834.00 1,698.00 1,942.00 1994M7 1994M8 1994M9 7.00000 6.90000 7.00000 1990M10 1994M10 7.00000 1990M11 1990M12 1994M11 6.90000 10.8000 10.8000 1994M12 1995M1 1995M2 6.70000 1991M1 1991M2 1991M3 1991M4 1991M5 10.4000 6.60000 10.4000 6.60000 10.3000 10.2000 10.1000 10.1000 9.40000 1995M3 6.50000 1995M4 6.40000 1995M5 1995M6 1995M7 6.30000 1991M6 6.20000 1991M7 6.10000 1991M8 9.50000 9.20000 8.80000 1995M8 6.00000 1995M9 5.90000 1991M9 1991M10 1995M10 1995M11 1995M12 6.00000 1991M11 1991M12 1992M1 1992M2 8.50000 5.90000 5.80000 8.30000 8.00000 1996M1 1996M2 1996M3 5.70000 7.80000 5.70000 1992M3 7.80000 5.70000 5.50000 5.60000 1992M4 7.70000 1996M4 1992M5 7.40000 1996MS 1992M6 7.20000 1996M6 5.40000 5.50000 5.60000 1992M7 7.50000 1996M7 1992M8 7.50000 1996M8 1992M9 1992M10 1992M11 7.30000 1996M9 5.40000 7.40000 1996M10 5.30000 7.20000 7.30000 7.40000 7.20000 7.20000 7.30000 7.20000 7.30000 7.40000 7.10000 1996M11 1996M12 1997M1 5.30000 5.30000 5.40000 5.20000 5.00000 5.30000 1992M12 1993M1 1993M2 1997M2 1997M3 1997M4 1997M5 1997M6 1993M3 1993M4 1993M5 5.20000 1993M6 5.30000 1993M7 1997M7 5.30000 1993M8 5.30000 1997M8 1997M9 1997M10 1997M11 1993M9 7.10000 5.30000 1993M10 1993M11 1993M12 7.20000 7.00000 7.00000 5.30000 5.30000