## (Solved) CONCORDIA UNIVERSITY Department of Economics ECON 222/4 SECTIONS C, D and EE STATISTICAL METHODS II WINTER 2017 - ASSIGNMENT 2 Due: Thursday, March...

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CONCORDIA UNIVERSITY
Department of Economics
ECON 222/4 SECTIONS C, D and EE
STATISTICAL METHODS II
WINTER 2017 â€“ ASSIGNMENT 2
Due: Thursday, March 23 before 5:00pm
Name __________________________________
question
marks 1 2 3 1. (38 marks) Consider the simple regression model population parameters and e~ iidN , 2 yi 1
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14 1
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8
10 a. (2 marks) Calculate b. (2 marks) Calculate b0 b1 . . c. (2 marks) Briefly interpret b0 5 . 1 yi 0 1 xi ei , where 0 and total are unknown
1
. Use the sample data given in the table below to answer the following questions.
xi 4 d. (2 marks) Briefly interpret xi yi 1
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14 1
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10 b1 . e. (2 marks) Calculate SST. f. (2 marks) Calculate SSR. g. (2 marks) Calculate SSE. h. (2 marks) Calculate the coefficient of determination, i. (2 marks) Briefly interpret R2 . 2 R2 . j. (2 marks) Calculate the correlation coefficient, r. k. (2 marks) Briefly interpret r. l. (2 marks) Calculate the standard error of the estimate, m. (2 marks) Calculate n. (2 marks) Calculate o. (2 marks) Calculate var b1 var b0 Ë† . . . cov b0 , b1 . p. (2 marks) Use the estimated regression line to predict y when x = 10. 3 q. (2 marks) Construct a 95Â­percent prediction interval for y when x = 10, using t 0.025,6 = 2.447 r. (2 marks) Construct a 95Â­percent confidence interval for , using t 0.025,6 = 2.447 s. (2 marks) Test, at the 5Â­pecent level of significance, whether Clearly state the null and alternative hypotheses, the test statistic and your conclusion. Use a
critical value t 0.025,6 = 2.447 4 2. (4 marks) Consider the standard linear regression model, Yi = 0 + 1 Xi + i with all classical
assumptions holding. Derive the Ordinary Least Squares (OLS) coefficient estimators for the model
above.
i. (2 marks) b0, the estimator of the intercept coefficient. (Show all steps) 5 ii. (2 marks) b1, the estimator of the slope coefficient. (Show all steps) 6 3. (6 marks) Briefly interpret a. (2 marks) b0 and b1 in each of the following equations. Ë†i b0 b1 ln xi
y b. (2 marks) lny
^i b0 b1 xi 7 c. (2 marks) ln
^
y i b b ln x
0
1
i 4. (8 marks) Consider the following regression models
and Yi = 0 + 1 Xi + i Yi * = 0* + 1* Xi* + i* Let Yi * = wYi where w is a constant. What is the relationship between
a. (2 marks) 0 and 0* b. (2 marks) 1 and 1* 8 c. (2 marks) var (0) and var ( 0*) d. (2 marks) var (1) and var ( 1*) e. (2 marks) standard deviation of (1) and standard deviation of ( 1*) 5. (8 marks) Complete textbook exercise 2.13. 9

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