For the following variables: AUTOTIME = Commute time via automobile in minutes B
ID: 3143680 • Letter: F
Question
For the following variables:
AUTOTIME = Commute time via automobile in minutes
BUSTIME = Commute time via bus in minutes
DTIME = BUSTIME - AUTOTIME
AUTO = 1 if automobile chosen, 0 if not
The output from Eviews is:
Table 1.1(Model 1) Dependent Variable: AUTO
Method: Least Squares
Date: 08/16/09 Time: 23:38
Sample: 1 21
Included observations: 21
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
0.484795
0.071449
6.785151
0.0000
DTIME
0.007031
0.001286
5.466635
0.0000
R-squared
0.611326
Mean dependent var
0.476190
Adjusted R-squared
0.590869
S.D. dependent var
0.511766
S.E. of regression
0.327343
Akaike info criterion
0.694776
Sum squared resid
2.035914
Schwarz criterion
0.794254
Log likelihood
-5.295144
Hannan-Quinn criter.
0.716365
F-statistic
29.88410
Durbin-Watson stat
1.978844
Prob(F-statistic)
0.000028
Table 1.2 (Model 2) Dependent Variable: AUTO
Method: ML - Binary Logit (Quadratic hill climbing)
Date: 08/17/09 Time: 23:19
Sample: 1 21
Included observations: 21
Convergence achieved after 5 iterations
Covariance matrix computed using second derivatives
Variable
Coefficient
Std. Error
z-Statistic
Prob.
C
-0.237575
0.750477
-0.316566
0.7516
DTIME
0.053110
0.020642
2.572866
0.0101
McFadden R-squared
0.575700
Mean dependent var
0.476190
S.D. dependent var
0.511766
S.E. of regression
0.306518
Akaike info criterion
0.777718
Sum squared resid
1.785110
Schwarz criterion
0.877197
Log likelihood
-6.166042
Hannan-Quinn criter.
0.799308
Restr. log likelihood
-14.53227
LR statistic
16.73246
Avg. log likelihood
-0.293621
Prob(LR statistic)
0.000043
Obs with Dep=0
11
Total obs
21
Obs with Dep=1
10
(a) Based on model 1 results: - Write down the estimated regression model, explain the meaning of slope coefficient.
- Calculate the predicted probability of a person choosing automobile transportation given that DTIME = 90. Comment on this result.
(b) Based on model 2 results: - Write down the estimated regression model.
- Calculate the predicted probability of a person choosing automobile transportation given that DTIME = 90.
- Estimate the marginal effect of an increase in the variable DTIME on the probability of a person choosing automobile transportation given that DTIME = 90. Explain the meaning of this result.
(c) Test the slope coefficient for statistical significance at the 5 percent level.
(d) Explain with full proofs why the estimated coefficients of the model 1 are unbiased and consistent but not efficient.
Table 1.1(Model 1) Dependent Variable: AUTO
Method: Least Squares
Date: 08/16/09 Time: 23:38
Sample: 1 21
Included observations: 21
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
0.484795
0.071449
6.785151
0.0000
DTIME
0.007031
0.001286
5.466635
0.0000
R-squared
0.611326
Mean dependent var
0.476190
Adjusted R-squared
0.590869
S.D. dependent var
0.511766
S.E. of regression
0.327343
Akaike info criterion
0.694776
Sum squared resid
2.035914
Schwarz criterion
0.794254
Log likelihood
-5.295144
Hannan-Quinn criter.
0.716365
F-statistic
29.88410
Durbin-Watson stat
1.978844
Prob(F-statistic)
0.000028
Explanation / Answer
a) y^ = 0.484795 + 0.007031 *Dtime
slope coefficient - when we increase DTIME by 1 unit, dependent variable change by b units that is 0.007031 .
when DTIME = 90
y^ = 0.484795 + 0.007031 *90
= 1.117585
b) y^ = -0.237575 +0.053110 *DTIME
when DTIME = 90
p^ =1 / (1 + exp( -0.237575 +0.053110 *90))
= 0.9894635
marginal effect -
for 1 % increase in DTIME , change in probability is 0.05311*100% = 5.311 %
c) for model 1
TS = 6.785151
p-value = 0.0000
since p-value < 0.05
the slope coefficient is statistically significant at the 5 percent level.
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