We first estimate the following model via OLS: children; = Bo + Bieduc; + B2age; + Bzage? + Bqurban; + u; Regression results OLS Estimation Summary =======--= Dep. Variable: children R-squared: Adj. R-squared: 0.4239 Estimator: OLS 0.4227 No. Observations: 1953 F-statistic: 1437.1 Date: Thu, Dec 09 2021 P-value (F-stat) 0.0000 Time: 15:26:40 Distribution: chi2(4) Cov. Estimator: unadjusted Parameter Estimates Parameter Std. Err. T-stat P-value Lower CI Оpper CI const educ 0.6500 0.0099 -5.2350 -0.0825 -6.5091 -10.014 0.0000 -7.7831 -0.1018 -10.298 0.0000 -0.1212 age 0.5123 0.0400 12.816 0.0000 0.4340 0.5907 -0.0053 0.0006 -8.8446 0.0000 -0.0064 -0.0041 agesq urban -0.3961 0.0832 -4.7617 0.0000 -0.5591 -0.2331 (i) Given a group of 200 30-year old women who live in an urban area, suppose 100 of them have 7 years of education and 100 of them have 8 years of education. What is the estimated difference in the number of children these two groups (grouped by number of years of education) of women are expected to have? (ii) Given a group of 200 women with 12 years of education and who live in a nonurban area, suppose 100 of them are 30 years old and 100 of them are 35 years old. What is the estimated difference in the number of children the 35-year old group is expected to have, relative to the 30-year old group? (iii) Given a group of 200 25-year old women with 10 years of education, suppose 100 of them live in an urban area and 100 of them live in a nonurban area. What is the estimated difference in the number of children these two groups (grouped by urban and nonurban) of women are expected to have?
We first estimate the following model via OLS: children; = Bo + Bieduc; + B2age; + Bzage? + Bqurban; + u; Regression results OLS Estimation Summary =======--= Dep. Variable: children R-squared: Adj. R-squared: 0.4239 Estimator: OLS 0.4227 No. Observations: 1953 F-statistic: 1437.1 Date: Thu, Dec 09 2021 P-value (F-stat) 0.0000 Time: 15:26:40 Distribution: chi2(4) Cov. Estimator: unadjusted Parameter Estimates Parameter Std. Err. T-stat P-value Lower CI Оpper CI const educ 0.6500 0.0099 -5.2350 -0.0825 -6.5091 -10.014 0.0000 -7.7831 -0.1018 -10.298 0.0000 -0.1212 age 0.5123 0.0400 12.816 0.0000 0.4340 0.5907 -0.0053 0.0006 -8.8446 0.0000 -0.0064 -0.0041 agesq urban -0.3961 0.0832 -4.7617 0.0000 -0.5591 -0.2331 (i) Given a group of 200 30-year old women who live in an urban area, suppose 100 of them have 7 years of education and 100 of them have 8 years of education. What is the estimated difference in the number of children these two groups (grouped by number of years of education) of women are expected to have? (ii) Given a group of 200 women with 12 years of education and who live in a nonurban area, suppose 100 of them are 30 years old and 100 of them are 35 years old. What is the estimated difference in the number of children the 35-year old group is expected to have, relative to the 30-year old group? (iii) Given a group of 200 25-year old women with 10 years of education, suppose 100 of them live in an urban area and 100 of them live in a nonurban area. What is the estimated difference in the number of children these two groups (grouped by urban and nonurban) of women are expected to have?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Problem 3. The effect of education on fertility.
The dataset for this question contains data on number of children, years of education, age,
and economic status, for women in Botswana during 1988.
Here is a description of the variables in the data set:
Variable Description
children
number of living children
age in years
square of age
years of education
husband's years of education
=1, if month born <= 6
=1, if live in urban area
=1, if has electricity
=1, if has tv
=1, if has bicycle
=1, if catholic
age
agesq
educ
heduc
frsthalf
urban
electric
tv
bicycle
catholic
Sample summary
children
age
agesq
educ
heduc
frsthalf
urban
electric
tv
bicycle
catholic
count 1953.000000 1953.000000 1953.000000 1953.000000 1953.000000 1953.000000 1953.000000 1953.000000 1953.000000 1953.000000 1953.000000
mean
3.455709
32.040451 1087.239631
5.084997
5.143881
0.568868
0.532002
0.166411
0.119304
0.302099
0.102919
std
2.293346
7.789751
523.421016
4.228725
4.803867
0.496361
0.499103
0.372544
0.324228
0.459286
0.303930
min
0.000000
16.000000
256.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
25%
2.000000
26.000000
676.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
50%
3.000000
31.000000
961.000000
5.000000
6.000000
1.000000
1.000000
0.000000
0.000000
0.000000
0.000000
75%
5.000000
38.000000 1444.000000
7.000000
8.000000
1.000000
1.000000
0.000000
0.000000
1.000000
0.000000
max
13.000000
49.000000 2401.000000
20.000000
20.000000
1.000000
1.000000
1.000000
1.000000
1.000000
1.000000
Sample correlation matrix
children
age
agesq
educ
heduc
frsthalf
urban
electric
tv
bicycle
catholic
children 1.000000 0.592830 0.569390 -0.308375 -0.267707
0.061648 -0.211916 -0.128381 -0.123450 0.075452 -0.015139
age 0.592830
1.000000 0.991967 -0.175734 -0.128130
0.021781 -0.128740
0.043577
0.063604
0.014338
0.028534
agesq 0.569390
0.991967
1.000000 -0.176230 -0.133899
0.022417 -0.129817
0.035344
0.054252
0.010605
0.023652
educ -0.308375 -0.175734 -0.176230
1.000000
0.647413 -0.139017
0.306733
0.460587
0.477218
0.090962
0.178140
heduc -0.267707 -0.128130 -0.133899
0.647413
1.000000 -0.121387
0.366976
0.455498
0.459974
0.067361
0.133010
frsthalf
0.061648
0.021781
0.022417 -0.139017 -0.121387
1.000000 -0.041554 -0.107937 -0.084674
0.036855 -0.031790
urban -0.211916 -0.128740 -0.129817
0.306733
0.366976 -0.041554
1.000000
0.328142
0.288223 -0.008674
0.081281
electric -0.128381
0.043577
0.035344
0.460587
0.455498 -0.107937
0.328142
1.000000
0.598972
0.089276
0.124656
tv -0.123450
0.063604
0.054252
0.477218
0.459974 -0.084674
0.288223
0.598972
1.000000
0.112188
0.135270
bicycle
0.075452
0.014338
0.010605
0.090962
0.067361
0.036855 -0.008674
0.089276
0.112188
1.000000
0.026710
catholic -0.015139
0.028534
0.023652
0.178140
0.133010 -0.031790
0.081281
0.124656
0.135270
0.026710
1.000000
Transcribed Image Text:We first estimate the following model via OLS:
children, 3D Bо + Bieduc, + Bzадe, + Bзaдe? + Bдurban, + u;
Regression results
OLS Estimation Summary
=========---- ------
============
=====
Dep. Variable:
children
R-squared:
Adj. R-squared:
0.4239
Estimator:
OLS
0.4227
No. Observations:
1953
F-statistic:
1437.1
Date:
Thu, Dec 09 2021
P-value (F-stat)
0.0000
Time:
15:26:40
Distribution:
chi2 (4)
Cov. Estimator:
unadjusted
Parameter Estimates
---------------------------------------=-------------------------------=------
Parameter
Std. Err.
T-stat
P-value
Lower CI
Upper CI
const
-6.5091
0.6500
-10.014
0.0000
-7.7831
-5.2350
educ
-0.1018
0.0099
-10.298
0.0000
-0.1212
-0.0825
age
0.5123
0.0400
12.816
0.0000
0.4340
0.5907
agesq
-0.0053
0.0006
-8.8446
0.0000
-0.0064
-0.0041
urban
-0.3961
0.0832
-4.7617
0.0000
-0.5591
-0.2331
====-
(i) Given a group of 200 30-year old women who live in an urban area, suppose 100 of
them have 7 years of education and 100 of them have 8 years of education. What
is the estimated difference in the number of children these two groups (grouped
by number of years of education) of women are expected to have?
(ii) Given a group of 200 women with 12 years of education and who live in a nonurban
area, suppose 100 of them are 30 years old and 100 of them are 35 years old.
What is the estimated difference in the number of children the 35-year old group
is expected to have, relative to the 30-year old group?
(iii) Given a group of 200 25-year old women with 10 years of education, suppose 100
of them live in an urban area and 100 of them live in a nonurban area. What is
the estimated difference in the number of children these two groups (grouped by
urban and nonurban) of women are expected to have?
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