*Number 3 ( 10pts) Say that we have the following model for avgscore, the average test score at an elementary school: avgscore=0+1expend+u where expend is the government expenditure per student, in thousands of dollars. (a) Explain why the error term E(u expend ) is likely not zero. What sign do you expect it will have? (As always, justify your answer.) (b) What direction of bias do you expect that ^1 will have in the above model? Explain. (c) In view of your answers above, what variable(s) might you want to add to your model to better estimate the effect of expend on test scores? Number 5(10pts) Define the following variables on a sample of firms: - rdintens: expenditures on research and development as a percentage of sales. - sales: sales in millions of dollars. - profmarg: profits as a percentage of sales. The data yields the following regression: (a) What is the interpretation of the coefficient of log( sales ) ? (b) Find a 95% confidence interval for the coefficient of profmarg. What conclusions can you draw from your calculation? *Number 3 ( 10pts) Say that we have the following model for avgscore, the average test score at an elementary school: avgscore=0+1expend+u where expend is the government expenditure per student, in thousands of dollars. (a) Explain why the error term E(u expend ) is likely not zero. What sign do you expect it will have? (As always, justify your answer.) (b) What direction of bias do you expect that ^1 will have in the above model? Explain. (c) In view of your answers above, what variable(s) might you want to add to your model to better estimate the effect of expend on test scores? Number 5(10pts) Define the following variables on a sample of firms: - rdintens: expenditures on research and development as a percentage of sales. - sales: sales in millions of dollars. - profmarg: profits as a percentage of sales. The data yields the following regression: (a) What is the interpretation of the coefficient of log( sales ) ? (b) Find a 95% confidence interval for the coefficient of profmarg. What conclusions can you draw from your calculation