Question

1. The true regression relationship is Y = β1 + β2X2 + β3X3 + u , and the coefficients are thought to have the following signs: β2 > 0 and β3 < 0. If the investigator omits X3 and instead estimates Y = δ1 + δ2X2 + v, then the coefficient on X2 will underestimate the effect of X2 on Y if the omitted variable X3 is negatively correlated with both X2 and Y.

True

False

Answer 1

True. because as X2 is positively correlated with X3 then omitting X3 will make the estimate of beta2 without affecting the Regression.The true relationship between dependent y and predictor x is linear,model errors are statistically independent, The errors are normally distributed with a 0 mean and constant standard deviation and The predictor x is non-stochastic and is measured error-free.

The expected value of Y is a linear function of the X variables. This means

• If Xchanges by an amount ∆X , holding other variables fixed, then the expected value of Y changes by a proportional amount β ∆X , for some constant β (which in general could be a positive or negative number).
• The value of β is always the same, regardless of values of the other X’s.
• The total effect of the X’s on the expected value of Y is the sum of their separate effects.