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# Regression Analysis

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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.])

3. If you were the owner of a business in the housing construction sector and you knew how interest rates were likely to change, how could you use this information to make better decisions?

Historical Data: Housing Starts in Relation to Interest Rates

Interest Rate* Housing Starts**

11% 9,000

10% 10,000

9% 24,000

8% 40,000

7% 52,000

6% 65,000

5% 80,000

4% 100,000

3% 130,000

2% 135,000

*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.

https://brainmass.com/math/interpolation-extrapolation-and-regression/regression-analysis-328114

#### Solution Summary

This Solution presents an extensive and detailed regression analysis on the given data. The regression analysis has been performed in EXCEL for better understanding.

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## Statistics Problems - Regression Analysis, Autocorrelation, Multicollinearity

1. Suppose an appliance manufacturer is doing a regression analysis, using quarterly time-series data, of the factors affecting its sales of appliances. A regression equation was estimated between appliance sales (in dollars) as the dependent variable and disposable personal income and new housing starts as the independent variables. The statistical tests of the model showed large t-values for both independent variables, along with a high r2 value. However, analysis of the residuals indicated that substantial autocorrelation was present.

a. What are some of the possible causes of this autocorrelation?

b. How does this autocorrelation affect the conclusions concerning the significance of the individual explanatory variables and the overall explanatory power of the regression model?

c. Given that a person uses the model for forecasting future appliance sales, how does this autocorrelation affect the accuracy of these forecasts?

d. What techniques might be used to remove this autocorrelation from the model?

2. Suppose the appliance manufacturer discussed in Exercise 1 also developed another model, again using time-series data, where appliance sales was the dependent variable and disposable personal income and retail sales of durable goods were the independent variables. Although the r2 statistic is high, the manufacturer also suspects that serious multicollinearity exists between the two independent variables.

a. In what ways does the presence of this multicollinearity affect the results of the regression analysis?

b. Under what conditions might the presence of multicollinearity cause problems in the use of this regression equation in designing a marketing plan for appliance sales?

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