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# Regression Analysis

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Find:
(a) explained variation
(b) unexplained variation
(c) total variation
(d) coefficient of determination
(e) standard error of estimates s^e

Listed below are budgets in millions of dollars and the gross receipts in millions of dollars from randomly selected movies.

Budget 62 90 50 35 200 100 90
Gross 65 64 48 57 601 146 47

Refer to the above and assume that the necessary conditions of normality and variance are met.

(f) Find the predicted gross amount for a movie with a budget of 100 million.
(g) Find 95% prediction interval estimate of the gross amount for a movie with a budget of 100 million.

https://brainmass.com/statistics/regression-analysis/regression-analysis-107966

#### Solution Summary

The solution gives the regression analysis for budgets and the gross receipts for selected movies. The answer contains:
a) explained variation
(b) unexplained variation
(c) total variation
(d) coefficient of determination
(e) standard error of estimates s^e

\$2.19

## 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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