solutions chapter 2 - 1 CHAPTER 2 Exercise Solutions...

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Unformatted text preview: 1 CHAPTER 2 Exercise Solutions Chapter 2, Exercise Solutions, Principles of Econometrics, 3e 2 EXERCISE 2.1 (a) x y x x ( ) 2 x x y y ( ) ( ) x x y y 3 5 2 4 3 6 2 2 1 1 0 0 1 3 0 0 1 0 1 2 2 4 0 0 0 2 1 1 4 4 i x = i y = ( ) i x x = ( ) 2 i x x = ( ) y y = ( ) ( ) x x y y = 5 10 0 10 0 10 1, 2 x y = = (b) ( ) ( ) ( ) 2 2 10 1. 10 x x y y b x x = = = 2 b is the estimated slope of the fitted line. 1 2 2 1 1 1. b y b x = = = 1 b is the estimated value of y when x = 0, it is the estimated intercept of the fitted line. (c) ( ) 5 2 2 2 2 2 2 1 3 2 1 1 15 i i x = = + + + + = ( ) ( ) 5 1 3 5 2 2 1 3 1 2 2 20 i i i x y = = + + + + = ( ) 5 5 2 2 2 2 1 1 15 5 1 10 i i i i x Nx x x = = = = = ( ) ( ) 5 5 1 1 20 5 1 2 10 i i i i i i x y Nxy x x y y = = = = = (d) i x i y i y i e 2 i e i i x e 3 5 4 1 1 3 2 2 3 1 1 2 1 3 2 1 1 1 1 2 0 2 4 2 0 2 1 3 9 0 i x = i y = i y = i e = 2 i e = i i x e = 5 10 10 0 16 0 (e) Refer to Figure xr2.1 below. Chapter 2, Exercise Solutions, Principles of Econometrics, 3e 3 Exercise 2.1 (continued) (f) -3-2-1 1 2 3 4 5 6-1.2-0.8-0.4 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 x y Figure xr2.1 Fitted line, mean and observations (g) 1 2 1 2 2, 1, 1, 1 y b b x y x b b = + = = = = Therefore: 2 1 1 1 = + (h) ( ) 4 3 2 0 1 /5 2 i y y N y = = + + + + = = (i) 2 2 16 5.3333 2 3 i e N = = = (j) ( ) n ( ) 2 2 2 5.3333 var .53333 10 i b x x = = = Chapter 2, Exercise Solutions, Principles of Econometrics, 3e 4 EXERCISE 2.2 (a) Using equation (B.30), ( ) 110 140 P X < < | $1000 | $1000 | $1000 2 2 2 | $1000 | $1000 | $1000 110 140 y x y x y x y x y x y x X P = = = = = = = < < ( ) 110 125 140 125 2.1429 2.1429 0.9679 49 49 P Z P Z = < < = < < = .00 .01 .02 .03 .04 .05 .06 100 110 120 130 140 150 Y FY Figure xr2.2 Sketch of PDF (b) Using the same formula as above: ( ) 110 140 P X < < ( ) 110 125 140 125 1.6667 1.6667 0.9044 81 81 P Z P Z = < < = < < = Chapter 2, Exercise Solutions, Principles of Econometrics, 3e 5 EXERCISE 2.3 (a) The observations on y and x and the estimated least-squares line are graphed in part (b). The line drawn for part (a) will depend on each students subjective choice about the position of the line. For this reason, it has been omitted. (b) Preliminary calculations yield: ( ) ( ) ( ) 2 21 44 22 17.5 7.3333 3.5 i i i i i x y x x y y x x y x = = = = = = The least squares estimates are ( ) ( ) ( ) 2 2 22 1.257 17.5 x x y y b x x = = = 1 2 7.3333 1.2571 3.5 2.9333 b y b x = = = 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 x y Figure xr2.3 Observations and fitted line Figure xr2....
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solutions chapter 2 - 1 CHAPTER 2 Exercise Solutions...

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