Data: Ramanathan 4-4, demand for bus travel.
1- Use method of OLS to estimate the parameters of the following model:
BUSTRAVL = β0+ β1FARE+ β2GASPRICE+ β3INCOME+ β4POP+ β5DENSITY+ β6LANDAREA+u
a. Do parameter estimates have the expected sign? Explain
Model 1: OLS, using observations 1-40
Dependent variable: BUSTRAVL
coefficient std. error t-ratio p-value
----------------------------------------------------------
const 2744.68 2641.67 1.039 0.3064
FARE −238.654 451.728 −0.5283 0.6008
GASPRICE 522.113 2658.23 0.1964 0.8455
INCOME −0.194744 0.0648867 −3.001 0.0051 ***
POP 1.71144 0.231364 7.397 1.69e-08 ***
DENSITY 0.116415 0.0595703 1.954 0.0592 *
LANDAREA −1.15523 1.80264 −0.6409 0.5260
Mean dependent var 1933.175 S.D. dependent var 2431.757
Sum squared resid 18213267 S.E. of regression 742.9113
R-squared 0.921026 Adjusted R-squared 0.906667
F(6, 33) 64.14338 P-value(F) 8.92e-17
Yes, all parameters have the correct sign;
As fares increase bus travel decreases (law of demand).
Increase in gas prices make bus travel relatively cheaper than driving.
Since bus travel is an inferior good, increase in income leads to less bus travel.
Increase in population leads to more bus travel.
Areas with high population density have more traffic congestions that make bus travel more efficient than
driving.
In metropolitan areas with large land area bus travel is time consuming hence driving becomes more
efficient.
b. Test for significance of POP at 1%. Show your work
H0: β4=0
H1: β4≠0,
Test statistic t=1.71/.23=7.397 with P-value=0.0000000169. So we reject the null.
c. Manually calculate SSR
Under ADD tab, define a new variable
ŷ= 2744-238.65FARE+ 533.11GASPRICE-0.194INCOME+1.71POP+0.116DENSITY-1.15LANDAREA
Then find sum(BUSTRAVEL-ŷ)2, it will be the same as SSR=18213267
This study source was downloaded by 100000850872992 from CourseHero.com on 02-21-2023 20:41:28 GMT -06:00
https://www.coursehero.com/file/16549389/CPS-4-solution/
1- Use method of OLS to estimate the parameters of the following model:
BUSTRAVL = β0+ β1FARE+ β2GASPRICE+ β3INCOME+ β4POP+ β5DENSITY+ β6LANDAREA+u
a. Do parameter estimates have the expected sign? Explain
Model 1: OLS, using observations 1-40
Dependent variable: BUSTRAVL
coefficient std. error t-ratio p-value
----------------------------------------------------------
const 2744.68 2641.67 1.039 0.3064
FARE −238.654 451.728 −0.5283 0.6008
GASPRICE 522.113 2658.23 0.1964 0.8455
INCOME −0.194744 0.0648867 −3.001 0.0051 ***
POP 1.71144 0.231364 7.397 1.69e-08 ***
DENSITY 0.116415 0.0595703 1.954 0.0592 *
LANDAREA −1.15523 1.80264 −0.6409 0.5260
Mean dependent var 1933.175 S.D. dependent var 2431.757
Sum squared resid 18213267 S.E. of regression 742.9113
R-squared 0.921026 Adjusted R-squared 0.906667
F(6, 33) 64.14338 P-value(F) 8.92e-17
Yes, all parameters have the correct sign;
As fares increase bus travel decreases (law of demand).
Increase in gas prices make bus travel relatively cheaper than driving.
Since bus travel is an inferior good, increase in income leads to less bus travel.
Increase in population leads to more bus travel.
Areas with high population density have more traffic congestions that make bus travel more efficient than
driving.
In metropolitan areas with large land area bus travel is time consuming hence driving becomes more
efficient.
b. Test for significance of POP at 1%. Show your work
H0: β4=0
H1: β4≠0,
Test statistic t=1.71/.23=7.397 with P-value=0.0000000169. So we reject the null.
c. Manually calculate SSR
Under ADD tab, define a new variable
ŷ= 2744-238.65FARE+ 533.11GASPRICE-0.194INCOME+1.71POP+0.116DENSITY-1.15LANDAREA
Then find sum(BUSTRAVEL-ŷ)2, it will be the same as SSR=18213267
This study source was downloaded by 100000850872992 from CourseHero.com on 02-21-2023 20:41:28 GMT -06:00
https://www.coursehero.com/file/16549389/CPS-4-solution/
