. use "E:\data\gpa2-1.dta"
. regress sat
hsize hsizesq
Source | SS
df MS Number of obs = 4137
-------------+------------------------------ F(
2, 4134) = 15.93
Model |
614822.097 2 307411.048
Prob > F =
0.0000
Residual |
79759024.2 4134 19293.4263 R-squared =
0.0076
-------------+------------------------------ Adj R-squared = 0.0072
Total |
80373846.3 4136 19432.7481 Root MSE =
138.9
------------------------------------------------------------------------------
sat | Coef.
Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
hsize |
19.81446 3.990666 4.97
0.000 11.99061 27.63831
hsizesq |
-2.130606 .549004 -3.88
0.000 -3.206949 -1.054263
_cons |
997.9805 6.203448 160.88
0.000 985.8184 1010.143
------------------------------------------------------------------------------
. * Yes the
quadratic term is statistically significant
. *The optimal
high school size
. gen logsat =
ln(sat)
. regress
logsat hsize hsizesq
Source | SS
df MS Number of obs = 4137
-------------+------------------------------ F(
2, 4134) = 16.19
Model |
.614405203 2 .307202602 Prob > F =
0.0000
Residual |
78.4287724 4134 .018971643 R-squared =
0.0078
-------------+------------------------------ Adj R-squared = 0.0073
Total |
79.0431776 4136 .01911102 Root MSE =
.13774
------------------------------------------------------------------------------
logsat | Coef.
Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
hsize |
.0196029 .0039572 4.95
0.000 .0118445 .0273612
hsizesq |
-.0020872 .0005444 -3.83
0.000 -.0031546 -.0010199
_cons |
6.896029 .0061515 1121.03
0.000 6.883969 6.908089
------------------------------------------------------------------------------
. *using the
logsat as the DV the optimal high school size is 469
. clear
. use
"E:\data\bwght2-1.dta"
. regress
lbwght lbwght npvis npvissq
Source | SS
df MS Number of obs = 1764
-------------+------------------------------ F(
3, 1760) = .
Model |
74.2054098 3 24.7351366 Prob > F =
.
Residual | 0
1760 0 R-squared =
1.0000
-------------+------------------------------ Adj R-squared = 1.0000
Total |
74.2054098 1763 .04209042 Root MSE =
0
------------------------------------------------------------------------------
lbwght | Coef.
Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
lbwght | 1 . .
. . .
npvis |
-7.94e-19 . .
. . .
npvissq |
-2.30e-20 . .
. . .
_cons |
-1.78e-15 . .
. . .
------------------------------------------------------------------------------
. regress
lbwght npvis npvissq
Source | SS
df MS Number of obs = 1764
-------------+------------------------------ F(
2, 1761) = 19.12
Model |
1.5771321 2 .788566048 Prob > F =
0.0000
Residual |
72.6282777 1761 .041242634 R-squared =
0.0213
-------------+------------------------------ Adj R-squared = 0.0201
Total |
74.2054098 1763 .04209042 Root MSE =
.20308
------------------------------------------------------------------------------
lbwght | Coef.
Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
npvis |
.0189167 .0036806 5.14
0.000 .0116979 .0261355
npvissq |
-.0004288 .00012 -3.57
0.000 -.0006641 -.0001934
_cons |
7.957883 .0273125 291.36
0.000 7.904314
8.011451
------------------------------------------------------------------------------
. *Yes the
quadratic term is statistically significant
. tab nvpis
variable nvpis
not found
r(111);
. tab npvis
total |
number of |
prenatal |
visits | Freq.
Percent Cum.
------------+-----------------------------------
0 | 5 0.28 0.28
1 | 2 0.11 0.40
2 | 5 0.28 0.68
3 | 12 0.68 1.36
4 | 6 0.34 1.70
5 | 27 1.53 3.23
6 | 59 3.34 6.58
7 | 58 3.29 9.86
8 |
117 6.63 16.50
9 | 96 5.44 21.94
10 | 199 11.28 33.22
11 | 115 6.52 39.74
12 | 618 35.03 74.77
13 | 72
4.08 78.85
14 | 97 5.50 84.35
15 | 143 8.11 92.46
16 | 41 2.32 94.78
17 | 12 0.68 95.46
18 | 15
0.85 96.32
19 | 4 0.23 96.54
20 | 35 1.98 98.53
21 | 5 0.28 98.81
22 | 2 0.11 98.92
23 | 1 0.06
98.98
24 | 2 0.11 99.09
25 | 3 0.17 99.26
26 | 1 0.06 99.32
30 | 7 0.40 99.72
33 | 1 0.06 99.77
35 | 1 0.06 99.83
36 | 1 0.06 99.89
40 | 2 0.11 100.00
------------+-----------------------------------
Total | 1,764
100.00
. gen visits =
.
(1832 missing
values generated)
. replace
visits = 1 if npvis >= 22
(89 real
changes made)
. tab visits
visits | Freq.
Percent Cum.
------------+-----------------------------------
1 | 89
100.00 100.00
------------+-----------------------------------
Total | 89
100.00
. tab npvis if
npvis >21
total |
number of |
prenatal |
visits | Freq.
Percent Cum.
------------+-----------------------------------
22 | 2 9.52 9.52
23 | 1 4.76 14.29
24 | 2 9.52 23.81
25 | 3 14.29 38.10
26 | 1 4.76 42.86
30 | 7 33.33 76.19
33 | 1 4.76 80.95
35 | 1 4.76 85.71
36 | 1 4.76 90.48
40 | 2 9.52 100.00
------------+-----------------------------------
Total | 21
100.00
. tab npvis
visits
total |
number of |
prenatal |
visits
visits | 1 |
Total
-----------+-----------+----------
22 | 2 | 2
23 |
1 | 1
24 | 2 | 2
25 | 3 | 3
26 | 1 | 1
30 | 7 | 7
33 | 1 | 1
35 | 1 | 1
36 | 1 | 1
40 | 2 | 2
-----------+-----------+----------
Total | 21 | 21
. *Yes it does
make sense in that if there are thatmany visits it could be a problemat
> ic
pregnancy with the likelihood of lower birth outcomes
. regress
lbwght npvis npvissq mage magesq
Source | SS
df MS Number of obs = 1764
-------------+------------------------------ F(
4, 1759) = 11.56
Model |
1.90136387 4 .475340968 Prob > F =
0.0000
Residual |
72.3040459 1759 .0411052 R-squared =
0.0256
-------------+------------------------------ Adj R-squared = 0.0234
Total |
74.2054098 1763 .04209042 Root MSE =
.20274
------------------------------------------------------------------------------
lbwght | Coef.
Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
npvis |
.0180374 .0037086 4.86
0.000 .0107636 .0253112
npvissq |
-.0004079 .0001204 -3.39
0.001 -.0006441 -.0001717
mage | .025392
.0092542 2.74 0.006
.0072417 .0435423
magesq |
-.0004119 .0001548 -2.66
0.008 -.0007154 -.0001083
_cons |
7.583713 .1370568 55.33
0.000 7.314901 7.852524
------------------------------------------------------------------------------
. *The optimal
age is 31
. gen age = .
(1832 missing
values generated)
. replace age =
1 if mage > 31
(605 real
changes made)
. replace age =
0 if mage <= 31
(1227 real
changes made)
. tab age
age | Freq.
Percent Cum.
------------+-----------------------------------
0 | 1,227 66.98 66.98
1 | 605 33.02 100.00
------------+-----------------------------------
Total | 1,832
100.00
. regress bwght
npvis npvissq mage magesq
Source | SS
df MS Number of obs = 1764
-------------+------------------------------ F(
4, 1759) = 8.59
Model |
11376019.1 4 2844004.78 Prob > F =
0.0000
Residual |
582383777 1759 331087.992 R-squared =
0.0192
-------------+------------------------------ Adj R-squared = 0.0169
Total |
593759796 1763 336789.448 Root MSE =
575.4
------------------------------------------------------------------------------
bwght | Coef.
Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
npvis |
37.47386 10.52531 3.56
0.000 16.83042 58.1173
npvissq |
-.7862864 .3417884 -2.30
0.022 -1.45664 -.1159322
mage |
81.60554 26.26395 3.11
0.002 30.09369 133.1174
magesq |
-1.327179 .4392829 -3.02
0.003 -2.18875
-.4656073
_cons |
1860.381 388.977 4.78
0.000 1097.475 2623.286
------------------------------------------------------------------------------
9.3
Let math10 denote the percentage of
students at a Michigan high school receiving a passing score on a standardized
math test (see also Ex 4.2). We are
interested in estimating the effect of per student spending on math
performance. A simple model is
i)
You
need to be “poor” to be in the federally funded student lunch program.
ii)
Because
lnchprg is negatively correlated with log(expend). It is significant.
iii)
Yes
iv)
Math10
would decrease by 3.24% if lunch program increase by 10%.
v)
It’s
a good predictor variable because R-squared is increasing.
9.4
(i)
Tvhours=
tvhours*+e0
(ii)
It’s not likely
to hold in the example, because if the tvhours=0 then they would be reported as
zero
So the error
depends on the actual tvhours
C9.1
(i)
. use
"C:\Users\sphl\Desktop\CEOSAL1-1.DTA"
. generate
rosneg = 0
. replace
rosneg = 1 if (ros<1)
(23 real
changes made)
. regress
lsalary lsales roe rosneg
Source | SS
df MS Number of obs = 209
-------------+------------------------------ F(
3, 205) = 28.81
Model |
19.7902019 3 6.59673397 Prob > F =
0.0000
Residual |
46.9319613 205 .228936397 R-squared =
0.2966
-------------+------------------------------ Adj R-squared = 0.2863
Total |
66.7221632 208 .320779631 Root MSE =
.47847
------------------------------------------------------------------------------
lsalary | Coef.
Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
lsales |
.2883868 .0336172 8.58
0.000 .222107 .3546665
roe |
.0166571 .0039681 4.20
0.000 .0088336 .0244806
rosneg |
-.225675 .109338 -2.06
0.040 -.4412462 -.0101038
_cons |
4.297602 .2932526 14.65
0.000 3.719425 4.87578
------------------------------------------------------------------------------
. ovtest
Ramsey RESET
test using powers of the fitted values of lsalary
Ho:
model has no omitted variables
F(3, 202) = 1.07
Prob > F = 0.3614
** We accept
the null-hypothesis
C9.8
1.
New update available; type -update all-
. use
"C:\Users\sphl\Desktop\twoyear.dta"
. codebook
stotal
--------------------------------------------------------------------------------------
stotal
total standardized test score
--------------------------------------------------------------------------------------
type: numeric (float)
range: [-3.3247969,2.2353656] units:
1.000e-09
unique values: 227 missing .: 0/6763
mean: .047483
std. dev: .853544
percentiles: 10% 25%
50% 75% 90%
-1.10531 -.327343 0
.610791 1.13706
. reg stotal jc
Source | SS
df MS Number of obs = 6763
-------------+------------------------------ F(
1, 6761) = 1.03
Model |
.752020193 1 .752020193 Prob > F =
0.3097
Residual |
4925.6191 6761 .728534108 R-squared =
0.0002
-------------+------------------------------ Adj R-squared = 0.0000
Total |
4926.37112 6762 .728537581 Root MSE =
.85354
------------------------------------------------------------------------------
stotal | Coef.
Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
jc | .013658
.0134431 1.02 0.310
-.0126946 .0400107
_cons |
.0428543 .0113348 3.78
0.000 .0206344 .0650741
------------------------------------------------------------------------------
. reg stotal
univ
Source | SS
df MS Number of obs = 6763
-------------+------------------------------ F(
1, 6761) = 1574.72
Model |
930.653211 1 930.653211 Prob > F =
0.0000
Residual |
3995.71791 6761 .590995106 R-squared =
0.1889
-------------+------------------------------ Adj R-squared = 0.1888
Total |
4926.37112 6762 .728537581 Root MSE =
.76876
------------------------------------------------------------------------------
stotal | Coef.
Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
univ |
.1615085 .00407 39.68
0.000 .15353 .1694869
_cons |
-.2636267 .0122004 -21.61
0.000 -.2875434 -.23971
------------------------------------------------------------------------------
. reg lwage jc
univ exper stotal
Source | SS
df MS Number of obs = 6763
-------------+------------------------------ F(
4, 6758) = 500.23
Model |
367.406832 4 91.8517079 Prob > F =
0.0000
Residual |
1240.88926 6758 .183617825 R-squared =
0.2284
-------------+------------------------------ Adj R-squared = 0.2280
Total |
1608.29609 6762 .237843255 Root MSE =
.42851
------------------------------------------------------------------------------
lwage | Coef.
Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
jc |
.0630514 .0068214 9.24
0.000 .0496792 .0764235
univ |
.0686405 .0025651 26.76
0.000 .0636121 .073669
exper |
.0048773 .0001571 31.04
0.000 .0045692 .0051854
stotal |
.0493766 .0068096 7.25
0.000 .0360277 .0627255
_cons |
1.495271 .0212176 70.47
0.000 1.453678 1.536864
------------------------------------------------------------------------------
. test jc +
univ <0
+ not found
r(111);
. test jc+
univ<0
+ not found
r(111);
. test jc <
univ
< not found
r(111);
. test jc +
univ < 0
+ not found
r(111);
. reg lwage jc
totcoll exper stotal
Source | SS
df MS Number of obs = 6763
-------------+------------------------------ F(
4, 6758) = 500.23
Model |
367.406831 4 91.8517079 Prob > F =
0.0000
Residual |
1240.88926 6758 .183617825 R-squared =
0.2284
-------------+------------------------------ Adj R-squared = 0.2280
Total |
1608.29609 6762 .237843255 Root MSE =
.42851
------------------------------------------------------------------------------
lwage | Coef.
Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
jc |
-.0055892 .0069385 -0.81
0.421 -.0191909 .0080126
totcoll |
.0686405 .0025651 26.76
0.000 .0636121 .073669
exper |
.0048773 .0001571 31.04
0.000 .0045692 .0051854
stotal |
.0493766 .0068096 7.25
0.000 .0360277 .0627255
_cons |
1.495271 .0212176 70.47
0.000 1.453678 1.536864
------------------------------------------------------------------------------
. gen stotalsq
= stotal * stotal
. reg lwage jc
univ exper stotal stotalsq
Source | SS
df MS Number of obs = 6763
-------------+------------------------------ F(
5, 6757) = 400.17
Model |
367.436832 5 73.4873664 Prob > F =
0.0000
Residual |
1240.85926 6757 .183640559 R-squared =
0.2285
-------------+------------------------------ Adj R-squared = 0.2279
Total |
1608.29609 6762 .237843255 Root MSE =
.42853
------------------------------------------------------------------------------
lwage | Coef.
Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
jc |
.0632092 .006833 9.25
0.000 .0498143 .0766041
univ |
.0685131 .0025846 26.51
0.000 .0634466 .0735797
exper |
.0048776 .0001572 31.04
0.000 .0045695 .0051857
stotal |
.0501562 .0070778 7.09
0.000 .0362814 .064031
stotalsq |
.0019191 .0047481 0.40
0.686 -.0073886 .0112268
_cons | 1.49399
.0214545 69.64 0.000
1.451932 1.536047
------------------------------------------------------------------------------
. gen jcstotal
= jc*stotal
. gen univtotal
= univ*stotal
. reg lwage jc
univ exper stotal jctotal univtotal
variable
jctotal not found
r(111);
. reg lwage jc
univ exper stotal jcstotal univtotal
Source | SS
df MS Number of obs = 6763
-------------+------------------------------ F(
6, 6756) = 334.24
Model |
368.126196 6 61.3543661 Prob > F =
0.0000
Residual |
1240.1699 6756 .183565704 R-squared =
0.2289
-------------+------------------------------ Adj R-squared = 0.2282
Total | 1608.29609
6762 .237843255 Root MSE =
.42845
------------------------------------------------------------------------------
lwage | Coef.
Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
jc | .063636
.0068983 9.22 0.000
.0501132 .0771588
univ |
.0689706 .0027439 25.14
0.000 .0635917 .0743494
exper |
.0048856 .0001572 31.08
0.000 .0045775 .0051938
stotal |
.0582108 .0087001 6.69
0.000 .0411559 .0752657
jcstotal |
-.0168818 .009275 -1.82
0.069 -.0350638 .0013001
univtotal |
-.0026652 .0029894 -0.89
0.373 -.0085254 .003195
_cons |
1.495924 .0212432 70.42
0.000 1.45428 1.537567
------------------------------------------------------------------------------
. test jcstotal
univtotal
( 1)
jcstotal = 0
( 2)
univtotal = 0
F(
2, 6756) = 1.96
Prob > F = 0.1410
. * not jointly
significant
. reg lwage jc
univ exper stotal
Source | SS
df MS Number of obs = 6763
-------------+------------------------------ F(
4, 6758) = 500.23
Model |
367.406832 4 91.8517079 Prob > F =
0.0000
Residual |
1240.88926 6758 .183617825 R-squared =
0.2284
-------------+------------------------------ Adj R-squared = 0.2280
Total |
1608.29609 6762 .237843255 Root MSE =
.42851
------------------------------------------------------------------------------
lwage | Coef.
Std. Err. t P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
jc |
.0630514 .0068214 9.24
0.000 .0496792 .0764235
univ |
.0686405 .0025651 26.76
0.000 .0636121 .073669
exper |
.0048773 .0001571 31.04
0.000 .0045692 .0051854
stotal |
.0493766 .0068096 7.25
0.000 .0360277 .0627255
_cons |
1.495271 .0212176 70.47
0.000 1.453678 1.536864
------------------------------------------------------------------------------
. * the
original regression is the preferred one
.