Q. Suppose a researcher is interested in estimating the impact of gasoline taxes (Xi) on every capital gallons of gasoline consumed every year (Yi). Suppose tax is measured in cents every gallon. The researcher has data from 51 states for a 10 year period for a total of 510 observations. The researcher estimates the linear OLS model Yi=β0 +β1 Xi+εi also calculates 1 ˆ = -0.90. Suppose instead of measuring taxes in cents every gallon, the researcher measures taxes in dollars every gallon where the new model is 2

Yi= γ0 +γ1Xi*+ εi also X*=X/100. Illustrate what will be the estimate on the coefficient on γ1? Suppose taxes are measured in cents as in the first case, but consumption is measured as gallons consumed every month, where Y*i=Yi/12. The model now is of the form Yi* =α1 + α2 Xi+εi. Illustrate what will be the estimate on α2?