# Question

Suppose that a regression relationship is given by the following:

Y = β0 + β1X1 + β2X2 + ε

If the simple linear regression of Y on X1 is estimated from a sample of n observations, the resulting slope estimate is generally biased for β1. However, in the special case where the sample correlation between X1 and X2 is 0, this will not be so. In fact, in that case the same estimate results whether or not X2 is included in the regression equation.

a. Explain verbally why this statement is true.

b. Show algebraically that this statement is true.

Y = β0 + β1X1 + β2X2 + ε

If the simple linear regression of Y on X1 is estimated from a sample of n observations, the resulting slope estimate is generally biased for β1. However, in the special case where the sample correlation between X1 and X2 is 0, this will not be so. In fact, in that case the same estimate results whether or not X2 is included in the regression equation.

a. Explain verbally why this statement is true.

b. Show algebraically that this statement is true.

## Answer to relevant Questions

Transportation Research, Inc., has asked you to prepare some multiple regression equations to estimate the effect of variables on fuel economy. The data for this study are contained in the data file Motors, and the dependent ...In Chapter 11, the regression of retail sales per household on disposable income per household was estimated by least squares. The data are given in Table 11.1, and Table 11.2 shows the residuals and the predicted values of ...Suppose that a regression was run with three independent variables and 30 observations. The Durbin Watson statistic was 0.50. Test the hypothesis that there was no autocorrelation. Compute an estimate of the autocorrelation ...An economist wants to estimate a regression equation relating demand for a product (Y) to its price (X1) and income (X2). It is to be based on 12 years of quarterly data. However, it is known that demand for this product is ...The following regression was fitted by least squares to 30 annual observations on time-series data: where yt = number of business failures x1t = rate of unemployment x2t = short-term interest rate x3t = value of new business ...Post your question

0