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# Regression analysis

Housing Starts II

For this case assignment we are going to look at housing starts again, but this time we are going to add another variable to the equation. The historical values below give interest rates, lumber prices (dollars per board-foot) and number of starts. We will compute a multiple regression equation using these variables, with starts as the DV. Interest and price are the IVs. Once you have computed the multiple regression equation, answer the following questions.

What is the regression formula that you computed? It should be of the form

Y = a1*X1 + a2*X2 + b

where

Y = number of housing starts
X1 = interest rates
a1 = regression coefficient of interest rates
X2 = lumber prices
a2 = regression coefficient of lumber prices
b = constant.
What would the approximate number of housing starts be at the following interest rates and lumber prices:

9.0% at \$1.00 per board foot

8.5% at \$1.50 per board foot

5.5% at \$1.25 per board foot

4.5% at \$0.90 per board foot

3.7% at \$1.00 per board foot

2.3% at \$0.75 per board foot.

As before, you'll need to use the regression equation to calculate the number of starts. Don't try to "guess" the answers using the historical data.

Historical values: Housing Starts in Relation to Interest Rates and Lumber Prices

Interest Rate Price Per Board Foot Housing Starts

11% \$1.25 8,500

11% \$1.00 9,000

11% \$0.90 9,200

11% \$0.75 9,500

10% \$1.25 9,700

10% \$1.00 10,000

10% \$0.90 10,300

9% \$1.25 22,000

9% \$1.00 24,000

8% \$1.25 39,000

8% \$0.90 45,000

8% \$0.75 52,000

Use the multiple regression app at Waner (2007), listed on the Background page, or click HERE to compute your multiple regression formula. (NOTE: Enter percentages as .08, .09, .10, etc. Do not enter "%", "\$", or "," .)

If you were the owner of a business in the housing construction sector how would this information affect your decisions?

Write a 3-4 page paper answering the above question

#### Solution Summary

Step by step method for regression analysis is discussed here. Regression coefficients, coefficient of determination, scatter diagram and significance of regression model are explained in the solution.

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