4. Use the data set ceosal1 available on canvas to answer this question. (75 points) (a) Estimate the model y=0+1x+u where y=log (salary) [here lsalary] and x=log (sales) [here lsales]. Estimate this model using the formulas for ^0 and ^1, not the built in OLS function of your statistical package. (25 points) (b) Calculate the standard errors of ^0 and ^1. Again, estimate these using the formulas, not the built in OLS function of your statistical package. (25 points) (c) Run a two-sided t-test on the null hypothesis H0:1=0. You can use any of the three versions of the t-test to test this hypothesis. (25 points) 5. Use the data set hprice3 available on canvas to answer this question. ( 75 points) (a) Estimate the multivariate regression model lprice =0+1 age +2 linst +3 rooms + 4 baths +5lsqft+6 lland +u. (Feel free to use the built in OLS function for these questions) (25 points) (b) Which of the coefficients you found in part (a) are statistically significant different from 0 ? How do you know this? (25 points) (c) Run an F-test dropping the statistically insignificant variables you found in part (b). Do these variables jointly help to explain the variation in y ? ( 25 points)