Question

for a dummy variable regression, female = 0, male =1......if we accidentally code the female = -1 instead of 0, what's the estimate of OLS of beta0 and beta1?

Answer 1

Solution: For a dummy variable regression, female = 0, male =1,if we accidentally code the female = -1 instead of 0, the estimate of OLS of $\beta_{0}$ and $\beta_{1}$ will be

Lets denote the estimate of OLS of beta0 and beta1 with correct coding that is female = 0, male =1

beta0 denoted by $b_{0}$

and beta1 denoted by $b_{1}$ .

And the estimate of OLS of beta0 and beta1 with incorrect coding that is female = -1, male =1

beta0 denoted by $\beta_{0}$

and beta1 denoted by $\beta_{1}$ .

Therefore the esimate of OLS of $\beta_{0}$ and $\beta_{1}$ will be:

$\beta_{0}=b_{0}+\left ( \frac{b_{1}}{2} \right )$

$\beta_{1}=\left ( \frac{b_{1}}{2} \right )$