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Regression Analysis

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Instructions: Choose one or more of the data sets A-I below, or as assigned by your instructor. Choose the dependent variable (the response variable to be "explained") and the independent variable (the predictor or explanatory variable) as you judge appropriate. Use a spreadsheet or a statistical package (e.g., MegaStat or MINITAB) to obtain the bivariate regression and required graphs. Write your answers to exercises 12.28 through 12.43 (or those assigned by your instructor) in a concise report, labeling your answers to each question. Insert tables and graphs in your report as appropriate. You may work with a partner if your instructor allows it.

12.50 In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks. (a) Write the fitted regression equation. (b) State the degrees of freedom for a twotailed test for zero slope, and use Appendix D to find the critical value at α = .05. (c) What is your conclusion about the slope? (d) Interpret the 95 percent confidence limits for the slope. (e) Verify that F = t2 for the slope. (f) In your own words, describe the fit of this regression.

R² 0.519
Std. Error 6.977
n 64

ANOVA table
____________________________________________________________________________
Source SS df MS F p-value
____________________________________________________________________________
Regression 3,260.0981 1 3,260.0981 66.97 1.90E-11
Residual 3,018.3339 62 48.6828
____________________________________________________________________________
Total 6,278.4320 63
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Regression output confidence interval
____________________________________________________________________________
Variables coefficients std. error t (df = 62) p-value 95% lower 95% upper
______________________________________________________________________________
Intercept 6.5763 1.9254 3.416 . 0011 2.7275 10.4252
X1 0.0452 0.0055 8.183 1.90E-11 0.0342 0.0563

(a) Write the fitted regression equation.
(b) State the degrees of freedom for a twotailed test for zero slope, and use Appendix D to find the critical value at α = .05. (c) What is your conclusion about the slope?
(d) Interpret the 95 percent confidence limits for the slope.
(e) Verify that F = t2 for the slope.
(f) In your own words, describe the fit of this regression.

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The solution provides step by step method for the calculation of regression analysis. The solution also provides conclusion about the slope and interpretation of the 95 percent confidence limits for the slope. Formula for the calculation and Interpretations of the results are also included.

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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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