TA Section 10, ECN 102 Spring Quarter 2015
Ilhyun Cho, ihcho@ucdavis.edu
June 3, 2015
STATA Code format
Question 1
Fill out all the remaining entries in this STATA output.
• (1) k − 1 = 3 − 1 = 2
• (2)
SS
df
=
540
2
= 270
• (3) T SS − ESS = RSS ⇒ 720 − RSS = 540 ⇒ RSS = 180
• (4) n − k = 21 − 3 = 18
• (5)
SS
df
=
• (6) F =
180
18
= 10
(RSSr −RSSu )/q
RSSu /(n−k)
=
(720−180)/2
180/18
= 27
• (7) dis Ftail(2,18, 27)
3.815e-06
• (8) R2 =
ESS
T SS
• (9) R̄2 = 1 −
=1−
RSS
T SS
RSS/(n−k)
T SS/(n−1)
Or R̄2 = R2 −
k−1
n−k (1
=
540
720
=1−
= 0.75
180/18
720/20
− R2 ) = 0.75 −
≈ 0.7222
2
18 (1
− 0.75) ≈ 0.7222
1
• (10) se =
• (11)
3
1.5
r
1
n−k
q
q
RSS
180
2 =
(y
−
y
ˆ
)
=
i
i
i=1
n−k
18 ≈ 3.1623
Pn
=2
• (12) dis 2*ttail(18, 1.5)
.15095045
• (13) dis invttail(18, 0.025)
2.100922
3 ± 2.100922 × 2
• (14)
2
1
=2
• (15) dis 2*ttail(18, 2)
.06082147
• (16) dis invttail(18, 0.025)
2.100922
2 ± 2.100922 × 1
• (17)
−4
1
= −4
• (18) dis 2*ttail(18,4)
.00083983
• (19) dis invttail(18, 0.025)
2.100922
−4 ± 2.100922 × 1
2
Question 2
Use data in file cobbdouglas.cvs for 25 factories.
• Do there appear to be any outliers?
graph box q
• Give a 95 % confidence interval for the population mean output.
su q
dis invttail(24, 0.025)
2.0638986
2405.835 ± 2.0638986 ×
2319.903
√
25
• Calculate the coefficient of variation for q, k, l.
su q k l
dis 2319.903/2405.835
.96428184
dis 3163.282/2843.944
1.112287
dis 340.3693/418.7168
.81288666
• twoway (scatter q k)(lfit q k)
• Following regression of output against capital, give a 95% confidence interval for the predicted value
of output when capital equals 4000.
su k
dis invttail(23, 0.025)
reg q k
368.3922 + .7164147 × 4000 ± 2.0686576 × 506.85 ×
3
q
1
25
+
(4000−2843.944)2
24×3163.2822
Question 3
• reg lnq lnk
Provide an interpretation of the coefficient of lnk in terms of elasticities.
A 1% increase in capital is associated with a .7333548% increase in output.
• Manually test at level 0.05 the claim that the coefficient of lnk equals 1.
dis (.7333548 -1)/.0528022
-5.0498881
dis ttail(23, 5.0498881)
.00002061
• reg lnq lnk lnl
Are the regressors lnk and lnl jointly statistically significant at level 0.05?
Yes. P rob > F = 0.0000
• Using STATA command test, test at level 0.05 whether returns to scale are constant. i.e. Test
whether the coefficients of lnl and lnk sum to one.
test lnk+ lnl =1
• gen lnk2 = lnk*lnk
gen lnl2 = lnl*lnl
gen lnlk = lnk*lnl
reg lnq lnk lnl
reg lnq lnk lnl lnk2 lnl2 lnlk
Which model do you prefer?
• reg lnq lnk lnl
reg lnq lnk lnl lnk2 lnl2 lnlk
Test whether lnk2 lnl2 lnlk are jointly statistically significant at level 0.05.
F =
(RSSr −RSSu )/q
RSSu /(n−k)
=
(.698021161−.52472881)/3
.52472881/19
≈ 2.0915913
dis Ftail(3,19, 2.0915913)
.13519636
4
• How do results change compared to you use option vce(robust)?
Question 4
• gen d1 = 1 if lotsize ==1
replace d1 =0 if d1==.
gen d2 = 1 if lotsize ==2
replace d2 =0 if d2==.
gen d3 = 1 if lotsize ==3
replace d3 =0 if d3==.
• reg price size lotsize
• reg price size
reg price size d2 d3
dis ((1.4975e+10 -1.4763e+10 )/2)/( 1.4763e+10 /25)
.17950281
dis Ftail(2,25, .17950281)
.83675316
• reg price size lotsize
reg price size d2 d3
Which one do you prefer?
• reg price size d1 d2
reg price size d2 d3
What happened?
• reg price size d1 d2
reg price size d2 d3
What happened?
Coefficients and standard errors and summary statistics unchanged except for the dummies.
• reg price size d1 d2 lotsize
What happened?
One of the regressors is dropped due to perfect collinearity.
5