Multiple Regression Analysis
Explain the steps on how to solve the problem below:
For this case 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
If you were the owner of a business in the housing construction sector how would this information affect your decisions?