Questio 1: Exercise 8. (a) Accordig to the regressio results i colum (1), the house price is expected to icrease by 1% ( 100% 0.0004 500 ) with a additioal 500 square feet ad other factors held costat. The 95% cofidece iterval for the percetage chage is 100% 500 (0.0004 1.96 0.000038) [17.76% to 4.74%]. (b) Because the regressios i colums (1) ad () have the same depedet variable, R ca be used to compare the fit of these two regressios. The log-log regressio i colum () has the higher R, so it is better so use l(size) to explai house prices. (c) The house price is expected to icrease by 7.1% ( 100% 0.071 1). The 95% cofidece iterval for this effect is 100% (0.071 1.96 0.034) [0.436% to 13.764%]. (d) The house price is expected to icrease by 0.36% (100% 0.0036 1 0.36%) with a additioal bedroom while other factors are held costat. The effect is ot statistically 0.0036 sigificat at a 5% sigificace level: t 0.09730 1.96. Note that this coefficiet 0.037 measures the effect of a additioal bedroom holdig the size of the house costat. Thus, it measures the effect of covertig existig space (from, say a family room) ito a bedroom. (e) The quadratic term l(size) is ot importat. The coefficiet estimate is ot statistically 0.0078 sigificat at a 5% sigificace level: t 0.05571 1.96. 0.14 (f) The house price is expected to icrease by 7.1% ( 100% 0.071 1) whe a swimmig pool is added to a house without a view ad other factors are held costat. The house price is expected to icrease by 7.3% ( 100% (0.071 1 0.00 1)) whe a swimmig pool is added to a house with a view ad other factors are held costat. The differece i the expected percetage chage i price is 0.%. The differece is ot statistically sigificat at 0.00 a 5% sigificace level: t 0.0 1.96. 0.10
Questio : Exercise 8.8 (a) ad (b) (c)
(d) (e)
Questio 3: Exercise 8.11 de( Y X ) X 1X Liear model: E(Y X) 0 1 X, so that 1 ad the elasticity is 1 dx E( Y X ) X Log-Log Model: E(Y X) 0 1 0 1 l( X ) u 0 1 l( X ) u 0 1 l( X ) E e X e E( e X ) ce, where c E(e u X), which does ot deped o X because u ad X are assumed to be idepedet. de( Y X ) ( ) 0 1 Thus 1 l( X E Y X ce ) 1, ad the elasticity is 1. dx X X Questio 4: Exercise 10.1 (a) With a $1 icrease i the beer tax, the expected umber of lives that would be saved is 0.45 per 10,000 people. Sice New Jersey has a populatio of 8.1 millio, the expected umber of lives saved is 0.45 810 364.5. The 95% cofidece iterval is (0.45 1.96 0.) 810 [15.8, 713.77]. (b) Whe New Jersey lowers its drikig age from 1 to 18, the expected fatality rate icreases by 0.08 deaths per 10,000. The 95% cofidece iterval for the chage i death rate is 0.08 1.96 0.066 [ 0.1014, 0.1574]. With a populatio of 8.1 millio, the umber of fatalities will icrease by 0.08 810.68 with a 95% cofidece iterval [0.1014, 0.1574] 810 [8.134, 17.49]. (c) Whe real icome per capita i New Jersey icreases by 1%, the expected fatality rate icreases by 1.81 deaths per 10,000. The 90% cofidece iterval for the chage i death rate is 1.81 1.64 0.47 [1.04,.58]. With a populatio of 8.1 millio, the umber of fatalities will icrease by 1.81 810 1466.1 with a 90% cofidece iterval [1.04,.58] 810 [840, 09]. (d) The low p-value (or high F-statistic) associated with the F-test o the assumptio that time effects are zero suggests that the time effects should be icluded i the regressio. (e) Defie a biary variable west which equals 1 for the wester states ad 0 for the other states. Iclude the iteractio term betwee the biary variable west ad the uemploymet rate, west (uemploymet rate), i the regressio equatio correspodig to colum (4). Suppose the coefficiet associated with uemploymet rate is ad the coefficiet associated with west (uemploymet rate) is. The captures the effect of the uemploymet rate i the easter states, ad captures the effect of the uemploymet rate i the wester states. The differece i the effect of the uemploymet rate i the wester ad easter states is. Usig the coefficiet estimate ( ˆ ) ad the stadard error SE( ˆ ), you ca calculate the t-statistic to test whether is statistically sigificat at a give sigificace level. Questio 5: Exercise 10.9 1 T (a) ˆ Y which has variace. Because T is ot growig, the variace is ot gettig i T t1 it small. ˆi is ot cosistet. u T (b) The average i (a) is computed over T observatios. I this case T is small (T 4), so the ormal approximatio from the CLT is ot likely to be very good.
Questio 6: Exercise 10.11 Usig the hit, equatio (10.) ca be writte as ˆ DM 1 i1 i1 1 1 4 4 1 1 i1 4 4 X X Y Y X X Y Y i i1 i i1 i i1 i i1 X X 1 Y Y 1 X X X X X X i i1 i i1 i i i i BA 1 i1 i i1 ˆ