Question One a) What assumptions underlie the least square method for the multiple regression? Explain why two perfectly multicollinear regressors cannot be included in a linear multiple regression. b) A Greenhill College participant interested in finding whether higher education has infleence one's standard of living considers fitting a regression model Yq=e+1X4+2Dq+j,i=I2n to 50 public servants pursuing different fields of study at GMMPA. The participant considers monthly salaries (Yi) as the regressand, years of experience (X2) and the level of education (D) as regressors. Below is an output of a regression analysis performed on data fetched from the above GIMPA participants. Regression Analysis: Y versus X,D The fegrientun equation in x=46001+5515x1032490 II 347426B=5q=1.7NJ= Ditlady =D:0O Anaipsio of Variahew From the above output i. Give a critical analysis of the model ii. Perform a test for 12 at 5% level of significance Question Two a) What are bomoskedasticity and heteroskedasticity in multiple linear regression? How would you check for heteroskedasticity in a multiple linear fegression model? b) Suppose that (Yi,Xi) satisfy the least square assumptions of a simple linear regression and that 1DN(0,2) and is independent of X,. A sample size of n=30 yields Y^i=43.2+61.5Xi,i=1,,30,R2=0.54,SER=1.52 (10.2) (7.4) Where the numbers in parenthesis are the homoskedastic-only standard errors for the regression coefficients. i. Construct a 99% confidence interval for e ii. Test H8:1=55 versus H1:1=55 at the 5% level iii. Test Hn:=55 versus H1:>55 at the 5% level iv. What is the estimate of q2 ? Question Three a) What is the significance of R and R2 of a regression model? b) The data below show consumption of chicken and its real price at GIMPA Calculate i. Does the real price of chicken depend on consumption or does consumption depend on the real price of chicken? Do you expect a positive or a negative relationship between these two variables? ii. X,X2,Y,Y2,XY iii. Sxx,Sn,Sxy and r-correlation coefficient iv. Find the least squares regression line by choosing appropriate dependent and independent variables based on your answer in part iii. v. Interpret the meaning of the values of a and b calculated in part iv. vi. Plot the scatter diagram and the regression line. vii. Calculate the r2 and explain what it means. viii. Predict the monthly consumption for a student with 10 Ghana cedis. ix. Compute the standard deviation of errors. x. Construct a 90% confidence interval for B. xi. Test at the 5% significance level whether B is negative