The following is from Gelman & Hill 2007:
Suppose that, for a certain population, we can predict log earnings from log - A person who is 66 inches tall is predicted to have earnings of $30,000. Every increase of 1% in height corresponds to a predicted increase of 0.8% in earnings. - The earnings of approximately 95% of people fall within a factor of 1.1 of predicted values. 1.Give the equation of the regression line and the residual standard deviation of the regression. 2.Suppose the standard deviation of log heights is 5% in this population. What, then, is the R2 of the regression model described here?
For the first question I would need a regression equation where log(Y) =intercept + 0.8*log(X) + error, where:
Y= earnings for people who have the height of 0 inches.
Beta= 0.8 increase in earnings with every inch of increase in height
I'm wondering if there's a simple way to calculate Y and the residual standard deviation...