Econ 2202 Test #3: Regression Analysis and Hypothesis Testing, Exams of Statistics

Download Econ 2202 Test #3: Regression Analysis and Hypothesis Testing and more Exams Statistics in PDF only on Docsity! TEST #3 – ECON 2202 – MARCH 23, 2010 – Professor Dubey INSTRUCTIONS: 1. The test lasts 1 hour and 20 minutes It is worth 100 marks, and contains two sections: a. Section A – 79 marks: 4 long-answer questions. Full explanations are required, including formulae used. You must use the 5-step method for all hypothesis tests unless otherwise stated. Round answers to 4 decimal places. b. Section B – 21 marks: 6 short-answer questions. No explanations required, though they may earn part- marks if your answer is incorrect or incomplete. PART A – 79 MARKS – 4 LONG ANSWER QUESTIONS. Show formulae and all work. 1. (27) An environmental study investigated the characteristics of a 9 landfills. For each plot they measured the "tonnage of garbage" dumped in the previous month, and the pollution emissions of toxic gas. The data are presented below, along with some summary statistics. Tonnage of garbage (x): 18 10 13 29 16 13 22 9 32 Amount of toxic gas (y): 7 10 14 28 12 9 10 11 25 ∑xi = 162, ∑yi = 126, ∑xiyi = 2648, ∑xi2= 3448, ∑yi2 = 2200, SSR=164.5714. a. (6) Consider the regression line relating y to x. Calculate the least squares estimates of the slope and intercept for the regression line relating amount of toxic gas, y, to tonnage of garbage, x. b. (5) Calculate SST and SSE. c. (6) Calculate se and sb1. d. (8) Perform a test of the hypothesis H0: β1 = 10. e. (2) The investigators plan to continue to examine additional landfills. If, tomorrow, they find a landfill whose tonnage of garbage dumped the previous month is 13, give a prediction of the amount of toxic gas that will be emitted. 2. (18) Using the information provided, answer the following: a. (8) For a sample of 66 months, the correlation between the returns on Canadian and Hong Kong T-bills was found to be 0.2930. Test the hypothesis that the population correlation is 0. Use α = 0.01. b. (8) An attempt was made to evaluate the Canadian inflation rate as a predictor of the Canadian T-bill rate. For the sample of 66 months of observations, the estimated linear regression ^y = 0.0027 + 0.7916x was obtained where y = change in the Canadian T-bill rate x = change in Canadian inflation rate sb1 = 0.2759 Test if the slope of the population regression line is 1. Use α = 0:01. c. (2) Could you have tested correlation between Canadian and Hong Kong T-bill rates using a simple linear regression? Explain why or why not. 1 3. (18) Given a simple linear regression analysis, suppose the fitted regression model uses the following information: ^yi = 8 + 10xi, and se = 11:23; xbar = 8; n = 44; ∑(xi -xbar)2 = 800. a. (4) State all assumptions required to use ordinary least squares. b. (7) For x=17, find the 95% prediction interval for y. c. (7) For x=17, find the 95% confidence interval for the expected value (or average value) of y. 4. (16) A collector of antique grandfather clocks knows that the price received for the clocks increases linearly with the age of the clocks. Moreover the collector hypothesizes that the auction price of the clocks will increase linearly as the number of bidders increases. For the sample of 32 auction prices (y) of grandfather clocks along with their age of clock in years (x1) and the number of bidders (x2), you are given the table below, and the information that SSR=516727, and SST=4799790. Coefficients Standard error Intercept -1338.95 173.80 Age 12.74 0.90 Number of bidders 85.95 8.72 a. (2) Write the population regression equation and the sample regression equation. b. (2) Interpret the slope and intercept of the sample regression equation. c. (4) Calculate the coefficient of determination, R2, and explain what its value means. d. (8) Use the F-test to test if the regression is significant. Use α = 0.01. 2