Economics 309 Final Exam Fall 2003
1. (20 points) Given that X is a random variable distributed normally with mean of 2 and variance of 25, find the following probabilities:
(a) Pr( X >= 2) "greater than or equal to 2"
(b) Pr( X < 0) "less than zero"
(c) Pr( X <= 4) "less than or equal to 4"
(d) Pr( 0 > X > 4) "lies between zero and four"
2. (40 points) The following is a printout from a regression analysis called a Hedonic study. These studies try to explain housing prices as function of various
factors, generally in 3 categories: characteristics of the house, characteristics of the neighborhood, and other factors that might impact housing prices (like being
close to a park, or an interstate highway). Even though there are many variables, concentrate on the following ones:
Dependent variable (Y): hprice = price at which house sold
Independent variables (Xs):
sarea = area of house in square feet
garage (dummy variable) = 1 if house has garage
fires = number of fireplaces in house
neigh1-5 = neighborhood dummy variables = 1 if house in particular neighborhood 1 through 5
zone1 (dummy) = 1 if house within 1 mile of toxic waste site
zone15 (dummy) = 1 if house within 1.5 miles of site
zone2 (dummy) = 1 if house within 2 miles of site
(all other houses are included in constant term to avoid dummy variable trap)
wtp76_85 (dummy) = 1 if house sold when waste treatment plant was operating in vicinity
westriv (dummy) = 1 if house on the west side of the river
qrt_int (dummy) = 1 if house within ¼ mile of I-25
qrt_rr (dummy) = 1 if house within ¼ mile of railroad tracks
yr76 – yr96 = year dummies 1976 through 1996. (1997 is reference year)
_cons = constant term (beta zero)
Referring to the output, answer the following questions.
(a) Make an assessment of the overall performance of the equation.
(b) About how much do people pay per square foot for houses in this area?
(c) Test the hypothesis that the waste treatment plant had a negative impact on housing prices.
(d) Do people like to live near railroad tracks?
Source | SS df MS Number of obs = 1348
-------------+------------------------------ F( 39, 1308) = 75.92
Model | 1.9280e+12 39 4.9435e+10 Prob > F = 0.0000
Residual | 8.5172e+11 1308 651158761 R-squared = 0.6936
-------------+------------------------------ Adj R-squared = 0.6845
Total | 2.7797e+12 1347 2.0636e+09 Root MSE = 25518
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hprice | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sarea | 44.00403 1.750466 25.14 0.000 40.57001 47.43806
beds | -843.0037 1072.955 -0.79 0.432 -2947.906 1261.898
garage | 7467.474 995.7244 7.50 0.000 5514.083 9420.866
carport | 1581.686 1652.438 0.96 0.339 -1660.032 4823.404
pitched | -1301.91 1555.016 -0.84 0.403 -4352.508 1748.689
fires | 9312.502 1710.66 5.44 0.000 5956.565 12668.44
neigh1 | -16362.84 3034.281 -5.39 0.000 -22315.43 -10410.25
neigh2 | 12630.25 3340.824 3.78 0.000 6076.294 19184.21
neigh3 | -7902.872 5064.717 -1.56 0.119 -17838.73 2032.984
neigh4 | -722.4958 2891.915 -0.25 0.803 -6395.794 4950.802
zone_5 | -6964.322 8515.901 -0.82 0.414 -23670.64 9741.995
zone1 | -9410.148 4165.198 -2.26 0.024 -17581.35 -1238.949
zone15 | -11100.84 2543.704 -4.36 0.000 -16091.03 -6110.655
zone2 | -6058.121 2236.409 -2.71 0.007 -10445.46 -1670.78
wtp76_85 | -6503.445 9000.712 -0.72 0.470 -24160.85 11153.96
westriv | -11423.87 2970.433 -3.85 0.000 -17251.2 -5596.533
qrt_int | -4117.803 2444.457 -1.68 0.092 -8913.289 677.6823
qrt_rr | -6899.64 3055.394 -2.26 0.024 -12893.65 -905.6312
yr76 | -19718.65 8237.418 -2.39 0.017 -35878.65 -3558.655
yr77 | -18730.29 4167.959 -4.49 0.000 -26906.9 -10553.67
yr78 | -7389.484 5058.999 -1.46 0.144 -17314.12 2535.154
yr79 | -12988.51 4613.717 -2.82 0.005 -22039.6 -3937.412
yr80 | -5656.76 5046.965 -1.12 0.263 -15557.79 4244.272
yr81 | -10828.24 4762.18 -2.27 0.023 -20170.59 -1485.898
yr82 | -21843.9 4357.69 -5.01 0.000 -30392.73 -13295.08
yr83 | -21070.33 4419.936 -4.77 0.000 -29741.26 -12399.39
yr84 | -15375.66 4110.87 -3.74 0.000 -23440.28 -7311.037
yr85 | -12555.51 4033.855 -3.11 0.002 -20469.04 -4641.973
yr86 | -2093.755 4398.469 -0.48 0.634 -10722.58 6535.071
yr87 | -5316.896 4211.237 -1.26 0.207 -13578.41 2944.621
yr88 | -9098.563 4699.41 -1.94 0.053 -18317.77 120.6419
yr89 | -4691.74 4312.866 -1.09 0.277 -13152.63 3769.152
yr90 | -15341.24 4888.629 -3.14 0.002 -24931.65 -5750.829
yr91 | -7582.129 4301.114 -1.76 0.078 -16019.97 855.7069
yr92 | -10289.94 4127.911 -2.49 0.013 -18387.99 -2191.892
yr93 | -7047.527 3962.991 -1.78 0.076 -14822.04 726.9861
yr94 | -9554.132 3818.88 -2.50 0.012 -17045.93 -2062.333
yr95 | 2479.836 3967.237 0.63 0.532 -5303.007 10262.68
yr96 | 2247.144 4257.156 0.53 0.598 -6104.456 10598.74
_cons | 39823.18 4825.582 8.25 0.000 30356.45 49289.91
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3. (30 points) Explain how White’s test for heteroscedasticity can be used to identify, and correct for, the problem. You can create an example, or present your argument in general terms (Xs and Ys.)