(f) Find the 95% confidence interval for the regression coefficient without the aid of the computer software as well as with the aid of the computer software. (g) Construct the prediction interval for the conditional mean of for a given X = X = 5 with the aid of the software. (h) Conduct diagnostic checks for the residuals by using the Durbin-Watson test, the Breusch- Pagan test, and the Jarque-Bera test. Please clearly explain your conclusions. 3. The Excel file (prices.xls) contains data on three variables, gas price)(), natural gas ("). and electricity (2) of a sample of 10 observations from 1996 to 2005. (a) Find the least-squares regression equation of on A and Z with the aid of Stata. [Hint: the regression equation isY # o #9 -* +3 27+ ] (b) Find the coefficient of determination,, with the aid of the computer software. What does the number in R2 imply? (c) Find the value of the F test. What does the F test say about the overall significance of this model? (d) Test the null hypothesis at the 0.05 significance level that the regression coefficient of the population regression? 1, is 0.0 versus the alternative hypothesis that the regression coefficient exceeds 0.0. (e) Test the null hypothesis at the 0.05 significance level that the regression coefficient of the population regression? 2, is 0.0 versus the alternative hypothesis that the regression coefficient exceeds 0.0. (f) Based on the estimated equation) = b, + b, X + b, Z, determine the estimated value of Y from the given values of X and Z. (g) Estimate the gas price at the natural gas of 9 and the electricity of 8. (h) Calculate the VIF for each independent variable. Is there any multi-collinearity problem in this regression? Please explain