South East European University Mentor: Prof.

Hyrije Abazi Alili

Econometrics Student: Fatlinda Kuqi Sulejmani

Solutions to computer exercises C1; C2; C3 and C4; CHAPTER 03; WOOLDRIDGE

C1
(i)
Significantly lower birth weight was observed at the time point with lower income.
Improvement in income revealed an almost linear increase in birth weight. ( (Family income
and low birth weight in term infants: A nationwide study in Israel)

Most likely sign for coefficient estimate of B2 must be positive (>0), because more income
for family typically means better nutrition for the mother and better prenatal care.
(ii)
It is negatively correlated. The sample correlation between cigs and faminc is come out to be
-0.1730, thus indicating a negative correlation.
. correlate faminc cigs
(obs=1,388)

faminc cigs

faminc 1.0000
cigs -0.1730 1.0000

(iii)

. reg bwght cigs

Source SS df MS Number of obs = 1,388

F(1, 1386) = 32.24
Model 13060.4194 1 13060.4194 Prob > F = 0.0000
Residual 561551.3 1,386 405.159668 R-squared = 0.0227
Adj R-squared = 0.0220
Total 574611.72 1,387 414.283864 Root MSE = 20.129

bwght Coef. Std. Err. t P>|t| [95% Conf. Interval]

cigs -.5137721 .0904909 -5.68 0.000 -.6912861 -.3362581

_cons 119.7719 .5723407 209.27 0.000 118.6492 120.8946
South East European University Mentor: Prof. Hyrije Abazi Alili
Econometrics Student: Fatlinda Kuqi Sulejmani

. reg bwght cigs faminc

Source SS df MS Number of obs = 1,388

F(2, 1385) = 21.27
Model 17126.2088 2 8563.10442 Prob > F = 0.0000
Residual 557485.511 1,385 402.516614 R-squared = 0.0298
Adj R-squared = 0.0284
Total 574611.72 1,387 414.283864 Root MSE = 20.063

bwght Coef. Std. Err. t P>|t| [95% Conf. Interval]

cigs -.4634075 .0915768 -5.06 0.000 -.6430518 -.2837633

faminc .0927647 .0291879 3.18 0.002 .0355075 .1500219
_cons 116.9741 1.048984 111.51 0.000 114.9164 119.0319

The regression with and without faminc can be seen as :

bwght= 119.77- 0.514cigs
n=1388
2
R =0.023
And,
bwght= 116.97- 0.463cigs +0.093faminc
n=1388
2
R =0.030
The effect of cigarette smoking is slightly smaller when faminc is added to the regression, but
the difference is not great. This is due to the fact cigs and faminc are not highly correlated,
and the coefficient on faminc is practically small.

C2
(i)
. reg price sqrft bdrms

Source SS df MS Number of obs = 88

F(2, 85) = 72.96
Model 580009.152 2 290004.576 Prob > F = 0.0000
Residual 337845.354 85 3974.65122 R-squared = 0.6319
Adj R-squared = 0.6233
Total 917854.506 87 10550.0518 Root MSE = 63.045

price Coef. Std. Err. t P>|t| [95% Conf. Interval]

sqrft .1284362 .0138245 9.29 0.000 .1009495 .1559229

bdrms 15.19819 9.483517 1.60 0.113 -3.657582 34.05396
_cons -19.315 31.04662 -0.62 0.536 -81.04399 42.414

The estimated regression equation is:

price= -19.32 +0.128sqrft+ 15.2 bdrms
n=88
2
R =0.63222
South East European University Mentor: Prof. Hyrije Abazi Alili
Econometrics Student: Fatlinda Kuqi Sulejmani

(ii)
Holding square footage constant, the above equation can be written as:
price= 15.2 bdrms
So, estimated price increases by 15.2 which means $15.200 because price measured in
thousands of dollars.
(iii)
From the equation given in part one: price= 0.128sqrft +15.20, here sqrft=140 and bdrms=1
Price= 0.128*140+15.2*1
=17.92+15.2
=33.12
Which means $33,120.
Because the size of the house is greater, it has a much larger effect than in (ii).

(iv)
Since r2=0.632, about 63.2% of the variation in price is explained by square footage and
number of bedrooms.
(v)
From the equation price= -19.32 +0.128sqrft+ 15.2 bdrms , here we have sqrft=2438 and
bdrms=4
Price= -19.32+ 0.128(2438) +15.20(4)
= 353.544
The predicted price is $353,544.

(vi)
From the above part the estimated value of the home based only on square footage and
number of bedrooms is $353,544. The actual selling price was $300,000 which suggests the
buyer underpaid by some margin. But, of course, there are many other features of a house
that affect price and have been not controlled here.

C3
(i)

. reg lsalary lsales lmktval

Source SS df MS Number of obs = 177

F(2, 174) = 37.13
Model 19.3365617 2 9.66828083 Prob > F = 0.0000
Residual 45.3096514 174 .260400295 R-squared = 0.2991
Adj R-squared = 0.2911
Total 64.6462131 176 .367308029 Root MSE = .51029

lsalary Coef. Std. Err. t P>|t| [95% Conf. Interval]

lsales .1621283 .0396703 4.09 0.000 .0838315 .2404252

lmktval .106708 .050124 2.13 0.035 .0077787 .2056372
_cons 4.620917 .2544083 18.16 0.000 4.118794 5.123041
South East European University Mentor: Prof. Hyrije Abazi Alili
Econometrics Student: Fatlinda Kuqi Sulejmani

The constant elasticity model equation is:

log(salary)= 4.62 +0.162 log(sales) +0.107 log(mktval)
n=177
2
R = 0.299

(ii)
. reg lsalary lsales lmktval profits

Source SS df MS Number of obs = 177

F(3, 173) = 24.64
Model 19.3509799 3 6.45032663 Prob > F = 0.0000
Residual 45.2952332 173 .261822157 R-squared = 0.2993
Adj R-squared = 0.2872
Total 64.6462131 176 .367308029 Root MSE = .51169

lsalary Coef. Std. Err. t P>|t| [95% Conf. Interval]

lsales .1613683 .0399101 4.04 0.000 .0825949 .2401416

lmktval .0975286 .0636886 1.53 0.128 -.0281782 .2232354
profits .0000357 .000152 0.23 0.815 -.0002643 .0003356
_cons 4.686924 .3797294 12.34 0.000 3.937425 5.436423

Profits cannot be included in logarithmic form because profits are negative for nine of the
companies in the sample. When added in levels form, it gives:
log(salary)= 4.69 +0.162 log(sales) +0.98 log(mktval) +0.000036profit
n=177
2
R =0.299
Predicted salary increases by about only 3.6%, because the coefficient on profits is very
small.

(iii)
. reg lsalary lsales lmktval profits ceoten

Source SS df MS Number of obs = 177

F(4, 172) = 20.08
Model 20.5768102 4 5.14420254 Prob > F = 0.0000
Residual 44.0694029 172 .256217459 R-squared = 0.3183
Adj R-squared = 0.3024
Total 64.6462131 176 .367308029 Root MSE = .50618

lsalary Coef. Std. Err. t P>|t| [95% Conf. Interval]

lsales .1622339 .0394826 4.11 0.000 .0843012 .2401667

lmktval .1017598 .063033 1.61 0.108 -.022658 .2261775
profits .0000291 .0001504 0.19 0.847 -.0002677 .0003258
ceoten .0116847 .005342 2.19 0.030 .0011403 .022229
_cons 4.55778 .3802548 11.99 0.000 3.807213 5.308347

Adding ceoten to the equation gives:

log(salary)= 4.56 +0.162 log(sales) +0.102 log(mktval) +0.000029profits +0.012 ceoten
n= 177
2
R =0.318
This means that one more year as CEO increases predicted salary by about 1.2%.
South East European University Mentor: Prof. Hyrije Abazi Alili
Econometrics Student: Fatlinda Kuqi Sulejmani

(iv)
. corr lmktval profits
(obs=177)

lmktval profits

lmktval 1.0000
profits 0.7769 1.0000

The sample correlation between log(mktval) and profits is about 0.78, which is high. As it is
known, this causes no bias in the OLS estimators, although it can cause their variances to be
large.

C4
(i)
. summarize atndrte priGPA ACT

Variable Obs Mean Std. Dev. Min Max

atndrte 680 81.70956 17.04699 6.25 100

priGPA 680 2.586775 .5447141 .857 3.93
ACT 680 22.51029 3.490768 13 32

The obtained minimum, maximum and average values for the three variables atndrte priGPA
and ACT have been written in the table above.

(ii)
. reg atndrte priGPA ACT

Source SS df MS Number of obs = 680

F(2, 677) = 138.65
Model 57336.7612 2 28668.3806 Prob > F = 0.0000
Residual 139980.564 677 206.765974 R-squared = 0.2906
Adj R-squared = 0.2885
Total 197317.325 679 290.59989 Root MSE = 14.379

atndrte Coef. Std. Err. t P>|t| [95% Conf. Interval]

priGPA 17.26059 1.083103 15.94 0.000 15.13395 19.38724

ACT -1.716553 .169012 -10.16 0.000 -2.048404 -1.384702
_cons 75.7004 3.884108 19.49 0.000 68.07406 83.32675

The estimated model:

atndrte = β 0 + β 1 priGTA + β 2 ATC

atndrte =75.70+ 17.26 priGTA -1.72 ATC

Here the intercept is 75.70 and it means that, for a student whose prior GPA is zero as well
as whose ATC score is zero, the predicted attendance rate is 75.7%. The intercept tells the
South East European University Mentor: Prof. Hyrije Abazi Alili
Econometrics Student: Fatlinda Kuqi Sulejmani

fixed predicted attendance rate when all independent variables are zero and so it can be
considered as useful.

(iii)
The coefficient on priGPA means that, if a student’s former GPA is one point greater, the
attendace rate is expected to be around 17.26% points greater. This results in fixed ATC. The
negative coefficient on ATC is conceivably a bit astonishing. Five extra points on the ATC is
predicted to worse the attendance by 5*1.72= 8.6 percentage points at a particular level of
priGPA.

(iv)
Using part (ii) from the estimated model, here with priGPA= 3.65 and ATC=20 the above
equation becomes:
atndrte= 75.70 +( 17.26* 3.65) – (1.72 *20)
=104.299
In general circumstances a student cannot have greater than a 100% attendance rate.
Yes, there is one student (no.604) with priGPA=3.65 and ATC= 20

(v)
For student A with priGPA=3.1 and ACT =21:
atndrte =75.70 +( 17.26* 3.1) – (1.72 *21)
=93.086

For student B with priGPA= 2.1 and ATC= 26

atndrte =75.70 +( 17.26* 3.1) – (1.72 *21)
=67.226
Thus, the difference in the attendance rates for student A and B is 93.086- 67.226= 25.86
South East European University Mentor: Prof. Hyrije Abazi Alili
Econometrics Student: Fatlinda Kuqi Sulejmani

REFERENCES:

1) Savitsky B;Radomislensky I;Frid Z;Gitelson N;Hendel T; (no date) Family income

and low birth weight in term infants: A nationwide study in Israel, Maternal and child
health journal. U.S. National Library of Medicine. Available at:
https://pubmed.ncbi.nlm.nih.gov/35129767/ (Accessed: October 31, 2022).