Final Assignment Please do NOT forget to write your name here. ECON 2202 Please submit your work at 3:00 p.m. sharp on Tuesday, April 12, 2016 to the T.A. (Viktoria Galociova) in Loeb B-848. Late submissions will not be accepted. 1 Instructions 1. Please type your assignment by using a word processor. If you choose to write, then please write clearly in ink. 2. It is also very important that you will hand in all your software outputs (e.g., tables and gures, etc.) 3. Please nd the PHStat/Stata installation instructions on your course outline. 4. If you are not sure how to do regression using a software, please watch the videos posted in the course outline and cuLearn. 5. Also please pay a close attention to academic plagiarism. If I nd two or more papers that look very similar, there will be a heavy penalty (a maximum of 50 points will be deducted from all the papers that look very similar.) 1 2 Questions 1. The Excel le (amazon.xls) contains data on the two variables, sales (Y ) and income (X) of a sample of 10 observations from 1995 to 2004. (a) Use PHStat to generate descriptive statistics of X and Y . Explain the statistical results that you have just obtained. (b) Construct a scatter diagram. (c) Find the least-squares regression line of Y on X with the aid of PHStat/Data Analysis Toolpak. (d) Find the least-squares regression line of X on Y with the aid of PHStat/Data Analysis Toolpak. (e) Test the null hypothesis at the 0.05 signicance level that the regression coecient of the population regression is 0.0 versus the alternative hypothesis that the regression coecient exceeds 0.0. Perform the test without the aid of the computer software as well as with the aid of the computer software. (f) Find the 95% condence interval for the regression coecient 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 Y for a given X = Xp = 5 with the aid of the software. 2. The Excel le (prices.xls) contains data on three variables, gas price (Y ), natural gas (X), and electricity (Z) of a sample of 10 observations from 1996 to 2005. (a) Find the least-squares regression equation of Y on X and Z with the aid of PHStat/Stata. [Hint: the regression equation is Y = 0 + 1 X + 2 Z + .] (b) Find the coecient of determination, R2 , with the aid of the computer software. What does the number in R2 imply? 2 (c) Find the value of the F test. What does the F test say about the overall signicance of this model? (d) Test the null hypothesis at the 0.05 signicance level that the regression coecient of the population regression, 1 , is 0.0 versus the alternative hypothesis that the regression coecient exceeds 0.0. (e) Test the null hypothesis at the 0.05 signicance level that the regression coecient of the population regression, 2 , is 0.0 versus the alternative hypothesis that the regression coecient exceeds 0.0. (f) Based on the estimated equation Y = b0 + b1 X + b2 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. 3. The Stata data le (elemapi.dta) contains data on 21 school-related variables in 400 U.S. schools. Please refer to the text le (elemapi description.txt) for a description of these variables. (a) Regress api00 on meals, acs k3, avg ed, and full with the aid of Stata. [Hint: the regression equation is Y = 0 + 1 X1 + 2 X2 + 3 X3 + 4 X4 + .] (b) Find the coecient of determination, R2 , 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 signicance of this model? (d) Test the null hypothesis at the 0.05 signicance level that the regression coecient of the population regression, 1 , is 0.0 versus the alternative hypothesis that this regression coecient is not 0.0. (e) Test the null hypothesis at the 0.05 signicance level that the regression coecient of the population regression, 2 , is 0.0 versus the alternative hypothesis that this regression 3 coecient is not 0.0. (f) Test the null hypothesis at the 0.05 signicance level that the regression coecient of the population regression, 3 , is 0.0 versus the alternative hypothesis that this regression coecient is not 0.0. (g) Test the null hypothesis at the 0.05 signicance level that the regression coecient of the population regression, 4 , is 0.0 versus the alternative hypothesis that this regression coecient is not 0.0. (h) Use Variance Ination Factor (VIF) to detect potential multi-collinearity. (i) Regress api00 on meals, acs k3, and full with the aid of Stata. [Hint: the regression equation is Y = 0 + 1 X1 + 2 X2 + 3 X3 + .] Use all your knowledge about multiple regression, compare this regression model with the model used in part (a). Which regression model perform better? Why? 4