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# ps3 - Problem Set 3 ECON 837 Prof Simon Woodcock Spring...

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Problem Set 3 ECON 837 Prof. Simon Woodcock, Spring 2006 Due: Friday Feb 10 These questions are based on the simple regression model: y i = ° + ±x i + " i (1) E [ " i ] = 0 ; E ° " 2 i ± = ² 2 ; E [ " i " j ] = 0 when i 6 = j: (2) 1. [Warmup Question, 2005 Midterm] You are studying the relationship between house size and selling price. Let Y i be the selling price of house i (in thousands of dollars) and X i its area (in square feet). On a random sample of 20 observations, you compute: P i Y i = 10525 : 8 P i ² Y i ° ° Y ³ 2 = 218087 P i ² X i ° ° X ³ ² Y i ° ° Y ³ = 594257 P i X i = 47193 P i ² X i ° ° X ³ 2 = 4325691 (a) Compute the least squares estimates of ° and ± in the regression: Y i = ° + ±X i + " i : Assume that the " i are independent and each is distributed N (0 ; ² 2 ) : (b) What does the least squares estimate of ± tell you about the relationship between house size and selling price? (c) Compute R 2 for this regression. What does this value of R 2 tell you? (d) Test the hypothesis that ± = 0 at the 5% level of signi°cance (use one test of your choice). Interpret the result of your test.

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