Consider the following regression estimates (XM4): Linear regression where lwage female _cons . Coefficient -.5466561 1.84796 Robust std. err. .0313767 .0188221 t Number of obs F(1, 1258) Prob> F R-squared Root MSE P>|t| -17.42 0.000 98.18 0.000 = = Iwage is the natural logarithm of wage, female = 1 if the person is female and 0 if the person is male. = = 1,260 303.54 0.0000 0.1915 .53478 [95% conf. intervall -.6082124 -.4850997 1.811034 1.884886 There are only male and females in this sample (no other genders). a) Interpret the female coefficient. b) Imagine you would use the same dataset and regress lwage on male, where male is a dummy variable that is 1 when the person is male and 0 if the person is female. In this regression, what will be the value of the male coefficient? c) Using the same data as in a) and b), what happens if you regress lwage on male and female? Why? (Hint: refer to a Multi Linear Regression assumption in your answer) Imagine you would like to estimate the effect of the amount of rainfall in a given month in a region on the number of cars that were caught speeding in that region in a given month. You have data on both variables for multiple months. For this estimation, you can write down the error term of the econometric model as a; + Uit. a) what kind of factors are captured in a;? Give a general explanation and one example of such a factor in the specific context described above. b) What kind of factors are captured in Uit? Give a general explanation and one example of such a factor in the specific context described above.