# HW2 - E Y i | X i = 48-2 55 X i Compute the stochastic...

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Econ 444 Elementary Econometrics (Winter 2010) HOMEWORK EXERCISE: 2 Due in class on Wednesday, Jan 27 1. State with reasons whether the following statements are true or false. (1.a) The stochastic error term ± i and the residual e i mean the same thing, and their values are the same in each application. (1.b) The residual e i is always zero for each i when OLS is correctly ap- plied to data (with no rounding oﬀ error). 2. Imagine that you have data on the demand of the CD at the price levels of \$9, \$12, an \$16 for three CD stores on various days. Suppose that the data were as follows: Table 1 Observed Demand for a CD Observation Price The observed number of copies of the CD demanded i X i Y i (1) (2) (3) 1 9 21 2 12 16 3 16 4 (2.a) Compute the OLS estimate of the slope coeﬃcient, ˆ β 1 . Then com- pute the OLS estimate of intercept, ˆ β 0 . (2.b) Write down the sample regression equation. Interpret the estimated regeression coeﬃcient ˆ β 1 . (2.c) Compute the OLS residual for each i . (2.d) Now suppose that the population regression is given by :

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Unformatted text preview: E ( Y i | X i ) = 48-2 . 55 X i Compute the stochastic error term. Compare OLS residuals with the ac-tual error term. Are they diﬀerent? Explain. 1 Q3. Sir Francis Galton, a cousin of James Darwin, examined the relationship between the height of children and their parents towards the end of the 19th century. It is from this study that the name regression originated. You decide to update his ﬁndings by collecting data from 110 college students, and estimate the following relationship: d Studenth i = 19 . 6 + 0 . 73 Midparh i S.E = (7 . 2) (0 . 10) N = 110 ,R 2 = 0 . 45 (1) where Studenth is the height of students in inches, and Midparh is the average of the parental heights. (a) Interpret the estimated coeﬃcient of Midparh , ˆ β 1 = 0 . 73. (b) Based on above results what is the prediction for the height of a child whose parents have an average height of 70.06 inches? 2...
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HW2 - E Y i | X i = 48-2 55 X i Compute the stochastic...

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