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problem using regression

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I can prove this problem using regression, but I don't have an equation for it. Please help, thanks!

a.) Suppose you multiply all X1 values by 2 in an equation with one independent variable (X1) and a constant. What will be the effect of this rescaling, if any, on the coefficients (SYMBOL1 and SYMBOL2) and their standard errors? Prove your answer mathematically (You are not supposed to use run/calculate a regression as a proof).

*(Please see attachment for proper symbols)

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a.) Suppose you multiply all X1 values by 2 in an equation with one independent variable (X1) and a constant. What will be the effect of this rescaling, if any, on the coefficients ( and ) and their ...

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Prove your answer mathematically (You are not supposed to use run/calculate a regression as a proof).

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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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