Wooldridge Solution chapter 3

C3.1 (i) (ii)

Positive Yes. Positive: High income, can buy more goods Negative: base on fatheduc, most family have high education and know the danger of smoking, so high income family with high education tend not to smoke CIGS 1.000000 -0.173045

CIGS FAMINC

(iii)

FAMINC -0.173045 1.000000

cigs Dependent Variable: BWGHT Method: Least Squares Date: 12/20/14 Time: 16:35 Sample: 1 1388 Included observations: 1388 Variable

Coefficient

Std. Error

t-Statistic

Prob.

C CIGS

119.7719 -0.513772

0.572341 0.090491

209.2668 -5.677609

0.0000 0.0000

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

0.022729 0.022024 20.12858 561551.3 -6135.457 32.23524 0.000000

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

118.6996 20.35396 8.843598 8.851142 8.846420 1.924390

faminc Dependent Variable: BWGHT Method: Least Squares Date: 12/20/14 Time: 16:37 Sample: 1 1388 Included observations: 1388 Variable

Coefficient

Std. Error

t-Statistic

Prob.

C CIGS FAMINC

116.9741 -0.463408 0.092765

1.048984 0.091577 0.029188

111.5118 -5.060315 3.178195

0.0000 0.0000 0.0015

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

C3.2

0.029805 0.028404 20.06282 557485.5 -6130.414 21.27392 0.000000

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

118.6996 20.35396 8.837772 8.849089 8.842005 1.921690

(i)

result: price = -19,315 + 0,128 sqrft + 15,198 bdrms Dependent Variable: PRICE Method: Least Squares Date: 12/20/14 Time: 16:50 Sample: 1 88 Included observations: 88 Variable

Coefficient

Std. Error

t-Statistic

Prob.

C SQRFT BDRMS

-19.31500 0.128436 15.19819

31.04662 0.013824 9.483517

-0.622129 9.290506 1.602590

0.5355 0.0000 0.1127

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) (ii) (iii) (iv) (v) (vi)

C3.3

0.631918 0.623258 63.04484 337845.4 -487.9989 72.96353 0.000000

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

$15.198,19

$ 33,17923 R2= 63% 354.600 Estimate price = 354.600 Since actual =300.000 Then =300.000-354.600=-54.600 (underpaid)

293.5460 102.7134 11.15907 11.24352 11.19309 1.858074

(i)

Log (salary) = B0 + B1 log (sales) + B3 log (mktval) Log (salary) = 4,621 + 0,162 log (sales) + 0,107 log (mktval) Dependent Variable: LSALARY Method: Least Squares Date: 12/20/14 Time: 19:38 Sample: 1 177 Included observations: 177 Variable

Coefficient

Std. Error

t-Statistic

Prob.

C LSALES LMKTVAL

4.620918 0.162128 0.106708

0.254408 0.039670 0.050124

18.16339 4.086899 2.128880

0.0000 0.0001 0.0347

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) (ii)

0.299114 0.291057 0.510294 45.30966 -130.5594 37.12852 0.000000

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

6.582848 0.606059 1.509146 1.562979 1.530979 2.092115

Log (salary) = B0 + B1 log (sales) + B3 log (mktval) + B3 profits Log (salary) = 4,687 + 0,161 log (sales) + 0,097 log (mktval) + 3,57*10-5 profits Dependent Variable: LSALARY Method: Least Squares Date: 12/20/14 Time: 19:42 Sample: 1 177 Included observations: 177 Variable

Coefficient

Std. Error

t-Statistic

Prob.

C LSALES LMKTVAL PROFITS

4.686924 0.161368 0.097529 3.57E-05

0.379729 0.039910 0.063689 0.000152

12.34280 4.043299 1.531333 0.234668

0.0000 0.0001 0.1275 0.8147

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

0.299337 0.287186 0.511686 45.29524 -130.5312 24.63628 0.000000

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

6.582848 0.606059 1.520127 1.591904 1.549237 2.096546

The R2 is almost the same, including variable profits only gives small influence to the model. 70% of variation in log salary is unexplained. (iii)

Log (salary) = B0 + B1 log (sales) + B3 log (mktval) + B3 profits + B4 ceoten Log (salary) = 4,558 + 0,162 log (sales) + 0,102 log (mktval) + 2,91*10-5 profits + 0,012 ceoten

Dependent Variable: LSALARY Method: Least Squares Date: 12/20/14 Time: 19:49 Sample: 1 177 Included observations: 177

C3.4 (i)

Descriptive stat ATNDRTE 81.70956 87.50000 100.0000 6.250000 17.04699 -1.578799 5.693665

PRIGPA 2.586775 2.560000 3.930000 0.857000 0.544714 0.161246 2.760582

ACT 22.51029 22.00000 32.00000 13.00000 3.490768 0.075404 2.645701

Jarque-Bera Probability

488.0774 0.000000

4.570791 0.101734

4.200994 0.122396

Sum Sum Sq. Dev.

55562.50 197317.3

1759.007 201.4684

15307.00 8273.928

680

680

Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis

(ii)

Observations 680 Estimate the model Atndrte = 75,70 + 17,261 prigpa – 1,717 act

The intercept of 75.70 is the predicted percent of classes attended for a student with 0 cumulative GPA prior to the current term and an ACT score of 0. I would not call this particular meaning “useful.” The intercept is useful, but its interpretation is not. Dependent Variable: ATNDRTE Method: Least Squares Date: 12/20/14 Time: 20:09 Sample: 1 680 Included observations: 680 Variable

Coefficient

Std. Error

t-Statistic

Prob.

C PRIGPA ACT

75.70041 17.26059 -1.716553

3.884108 1.083103 0.169012

19.48978 15.93624 -10.15640

0.0000 0.0000 0.0000

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) (iii)

(iv)

(v)

C3.5

0.290581 0.288486 14.37936 139980.6 -2776.115 138.6513 0.000000

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

81.70956 17.04699 8.173867 8.193817 8.181589 2.010991

Additional point for GPA will increase the class attendance. However, additional score for ACT test will decrease the class attendance. Unexpected result. Perhaps gaining high score means that student thinks they do not have the necessity to attend the class

104,36 would seem to be a very good student. But no student attends more than 100% of classes! (observation number 569). The model provides residual The difference in predicted attendance between Student A and Student B is 93.09 - 67.23= 25.86%

log(wage) =0.284+ 0.092 educ + 0.0041 exper + 0.022 tenure. Dependent Variable: LWAGE Method: Least Squares Date: 12/20/14 Time: 20:35 Sample: 1 526 Included observations: 526 Variable

Coefficient

Std. Error

t-Statistic

Prob.

C EDUC EXPER TENURE

0.284360 0.092029 0.004121 0.022067

0.104190 0.007330 0.001723 0.003094

2.729230 12.55525 2.391437 7.133071

0.0066 0.0000 0.0171 0.0000

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

0.316013 0.312082 0.440862 101.4556 -313.5478 80.39092 0.000000

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

1.623268 0.531538 1.207406 1.239842 1.220106 1.768805

Partialling out on educ coefficient What we are doing is trying to find the effect of educ on log(wage), controlling for exper and tenure This effect is equal to the effect on log(wage) of the portion of educ that is NOT explained by exper and tenure. First we need to construct a variable that is equal to the portion of educ that is not explained by exper and tenure. The easiest way to do that is to take the residual from the regression: Educ = g0 + g1 exper + g2 tenure + u Educ = 13,574 – 0,074 exper + 0,048 tenure Dependent Variable: EDUC Method: Least Squares Date: 12/20/14 Time: 20:41 Sample: 1 526 Included observations: 526 Variable

Coefficient

Std. Error

t-Statistic

Prob.

C EXPER TENURE

13.57496 -0.073785 0.047680

0.184324 0.009761 0.018337

73.64710 -7.559282 2.600162

0.0000 0.0000 0.0096

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

0.101342 0.097906 2.629980 3617.483 -1253.487 29.48955 0.000000

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

To find the residuals in this regression I subtract educ from educ:

Dependent Variable: LWAGE

12.56274 2.769022 4.777517 4.801843 4.787042 1.869826

C3.6 (i) EDUC

3.533829

0.192210

18.38530

0.0000

EDUC

0.059839

0.005963

10.03492

0.0000

EDUC IQ

0.039120 0.005863

0.006838 0.000998

5.720784 5.875413

0.0000 0.0000

(ii)

(iii)

(iv)

C3.7

(i) Dependent Variable: MATH10 Method: Least Squares Date: 12/20/14 Time: 21:16 Sample: 1 408 Included observations: 408 Variable

Coefficient

Std. Error

t-Statistic

Prob.

C LEXPEND LNCHPRG

-20.36076 6.229691 -0.304585

25.07287 2.972634 0.035357

-0.812063 2.095680 -8.614468

0.4172 0.0367 0.0000

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

0.179927 0.175877 9.526228 36753.36 -1497.073 44.42926 0.000000

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

24.10686 10.49361 7.353301 7.382795 7.364972 1.902822

math10 = -20,36 + 6,23 lexpend – 0,305 lnchprg The sign of the coefficients are as expected: the percentage of students passing a math exam is increasing in expenditure per student and decreasing in the percentage of students who are in a school lunch program (presumably a subsidized lunch program) (ii) (iii)

No. for lexpend cannot set to 0 because log 0 = undefined. At least $1 for lexpend. For lnchprg we can set it to 0 Math10 with lexpend

Dependent Variable: MATH10 Method: Least Squares Date: 12/20/14 Time: 21:27 Sample: 1 408 Included observations: 408 Variable

Coefficient

Std. Error

t-Statistic

Prob.

C LEXPEND

-69.34108 11.16439

26.53013 3.169011

-2.613673 3.522990

0.0093 0.0005

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

0.029663 0.027273 10.34953 43487.76 -1531.396 12.41146 0.000475

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

24.10686 10.49361 7.516649 7.536312 7.524429 1.614623

The magnitude of the slope coefficient has gotten larger. It was previously 6.23 and is now 11.16. This speaks to a negative correlation between log(expend) and lnchprg. (iv)

correlation between lexpend log(expend) and lnchprg

LEXPEND LNCHPRG

LEXPEND 1.000000 -0.192704

LNCHPRG -0.192704 1.000000

student spends more for lexpend than lnchprg. Negative correlation (v)

C3.8

the inclusion of lnchprg suppressed the coefficient on log(expend) (1) when lnchprg increases, math10 decreases; (2) when lexpend increases, lnchprg decreases. Therefore, when lexpend increases, what happens, in total? When lexpend increases, lnchprg decreases, which causes math10 to go . . . up.

(i)

descriptive stat PRPBLCK 0.113486 0.041444 0.981658 0.000000 0.182416 2.700012 10.56841

INCOME 47053.78 46272.00 136529.0 15919.00 13179.29 0.962831 7.551386

Jarque-Bera Probability

1473.100 0.000000

416.2135 0.000000

Sum Sum Sq. Dev.

46.41594 13.57651

19244998 7.09E+10

Observations

409

409

Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis

prpblck = percentage income = dollar (ii) Psoda = 0,956 + 0,115 prpblck + 1,6*10-6

Dependent Variable: PSODA Method: Least Squares Date: 12/20/14 Time: 21:39 Sample: 1 410 Included observations: 401 Variable

Coefficient

Std. Error

t-Statistic

Prob.

C PRPBLCK INCOME

0.956320 0.114988 1.60E-06

0.018992 0.026001 3.62E-07

50.35379 4.422515 4.430130

0.0000 0.0000 0.0000

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

0.064220 0.059518 0.086115 2.951465 415.7934 13.65691 0.000002

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

1.044863 0.088798 -2.058820 -2.028940 -2.046988 1.696180

The coefficient on prpblck is 0.1149882. The literal interpretation would be: when prpblck increases by 1, the price of a medium soda increases by 11 cents. The only problem is, the notion of increasing prpblck by 1 is not very meaningful. prpblck is the proportion of individuals in a zip code who are black cannot increase by 1 unless the proportion of individuals in a zip code starts out as 0. That is, the only zip code that can increase by 1 is a zip code that starts out with no individuals who are black, and then becomes a zip code that is made up only of individuals who are black. This is not a very useful marginal effect. In order to interpret the marginal effect more usefully, look at smaller (more realistically-sized) changes. For instance, an increase of 0.01 (an increase of 1 in the percentage of individuals who are black in a zip code) is predicted to increase the price of a medium soda by 0.1149882 × 0.01 = 0.00114988,

C4.1 (i) (ii) (iii)

As expenditure of candidate A increases for 1%, percentage of vote for candidate A will increase for B1/100 H0: B1=-B2 or H0: B1+B2=0 1% increases expendA and 1% increases expendB leaves voteA unchanged Estimate model voteA = 45,079 + 6,083 lexpendA – 6,615 lexpendB + 0,152 prtystrA

Dependent Variable: VOTEA Method: Least Squares Date: 12/21/14 Time: 16:52 Sample: 1 173 Included observations: 173 Variable

Coefficient

Std. Error

t-Statistic

Prob.

C LEXPENDA LEXPENDB PRTYSTRA

45.07893 6.083316 -6.615417 0.151957

3.926305 0.382150 0.378820 0.062018

11.48126 15.91866 -17.46321 2.450210

0.0000 0.0000 0.0000 0.0153

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

0.792557 0.788874 7.712335 10052.14 -596.8609 215.2266 0.000000

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

50.50289 16.78476 6.946369 7.019277 6.975948 1.604129

Yes, 1% increases on expend A will probably increase vote for A. 1% increases on expend B will decrease vote for A. (iv)

t-test tB1-B2=(6,083-(-6,615)) / (0,382-0,379)