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

 

------------------------------------------------------------------------------

      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

------------------------------------------------------------------------------

 

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.)

 

Return to 309 homepage