# Question: Suppose that a regression relationship is given by the following Y

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.

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