For this case, we will examine some hypothetical data concerning interest rates and the number of housing starts per month. A new "housing start" is counted when a contractor begins construction of a new private house.
Create a scatterplot with interest rates on the X-axis and the number of housing starts on the Y-axis. (For information about how to do this, use the Excel "Help" utility and enter "Scatterplot." Then I would like you to compute a simple regression formula using the interest rates and number of housing starts provided below. Use the regression calculator found at Waner (2007). Once you have found your regression formula, answer the following questions.
1. What is the regression equation that you computed? The equation should have the form Y = m*X + B, were Y is the number of starts, X is the interest rate expressed as a decimal (e.g., 5% = 0.05), and B is the regression constant. (B is the hypothetical value of Y when X = 0. It may or may not make any practical sense, depending on the nature of the problem.)
2. What would the approximate number of housing starts be at the following interest rates: 8.5%, 4.5%, 3.7%, 2.3%? These must be CALCULATED, using the regression equation found above. (HINTS: Do NOT simply "guess" values, based on the historical data given below. That's wrong. Don't use linear interpolation between the historical data values; that's also wrong. Round off estimates of starts to the nearest whole number. [A house-building project either starts in a given month, or it doesn't. Therefore, it makes no sense to talk about fractions of a start.])
Historical Data: Housing Starts in Relation to Interest Rates
Interest Rate* Housing Starts**
*HINT: Enter interest rates into the regression app as decimals; e.g., 0.11, not 11%. Don't use the "%" sign!
**ANOTHER HINT: Do NOT include commas when entering your data into the regression app. Example: enter 9000, NOT 9,000.
This Solution presents an extensive and detailed regression analysis on the given data. The regression analysis has been performed in EXCEL for better understanding.