Quantitative Research Methods - Analysis of Factors Influencing Marital Quality of Women

This analysis examines the factors that influence the marital quality of women using quantitative research methods. The dependent variable is marital quality measured on a 7-point scale, while the key independent variable is the husband's income measured in 1,000 USD per month. The regression analysis shows a positive relationship between husband's income and marital quality. The model is further improved by controlling for husband's education and work hours.

Quantitative Research Methods
Student Name:
Instructor Name:
Course Number:
30 October 2018

1. (5 points) To begin with, understand the policy question.
a. (3 points) What is the policy question of this analysis? What is the dependent variable
and how is it measured? What is the key independent variable and how is it
measured?
Answer
What factors influence the marital quality of women? The dependent variable is the
marital quality and it is measured on a 7-point scale ranging from 1 to 7. The key
independent variable is the husband’s income measured in 1,000 USD per month.
b. (2 points) What is the population? What is the sample?
Answer
The population is all the Korean women aged between 20 and 64 while the sample is
a survey of 2,682 women surveyed in the 2007 for the population.
2. (4 points) Write a short paragraph which summarizes the distribution of the dependent
variable and the distribution of the key independent variable using summary statistics.
Answer
The average marital quality of the sampled women was found to be 5.38 with the highest
and the lowest marital quality recorded being 7 and 1 respectively. On the other hand, the
average husband’s income per month was found to be 2,748.5 US dollars per month with
the highest and lowest income recorded being 10,000 US dollars and 300 US dollars per
month.
hinc 2604 2.748522 1.291823 .3 10
maritalq 2676 5.381913 1.150974 1 7
Variable Obs Mean Std. Dev. Min Max
. summarize maritalq hinc

3. (6 points) Before conducting regression analysis, it is valuable to examine the
relationship between hinc and maritalq with simple graphical and numerical summary.
a. (1 point) Calculate the correlation between hinc and maritalq.
Answer
2599 2604
0.0000
hinc 0.1574 1.0000
2676
maritalq 1.0000
maritalq hinc
. pwcorr maritalq hinc, obs sig
b. (2 points) Draw a scatter plot between hinc and maritalq.
Answer
0 2 4 6 8
Marital Quality
0 2 4 6 8 10
Husband’s income (in 1,000 USD per month)
A scatter plot of marital quality versus husband's income
c. (1 point) Based on what you find in Q3.a and Q3.b, how do you think the two
variables are related?
Answer

The above results shows that there is a weak positive non-linear relationship between
husband’s income and the marital quality. The two variables are positively related as
can be seen from the correlation test and the scatterplot.
d. (2 point) Is there any evidence of a non-linear relationship in the scatter plot? If so,
describe the non-linearity.
Answer
Yes there is evidence of non-linear relationship. The non-linearity exhibited is the
positive non-linearity between the two variables (husband’s income and marital
quality).
4. (13 points) Now let’s examine the relationship with a regression with no control variable.
Output
_cons 5.007391 .0524165 95.53 0.000 4.904609 5.110174
hinc .1402914 .0172685 8.12 0.000 .10643 .1741527
maritalq Coef. Std. Err. t P>|t| [95% Conf. Interval]
Total 3435.90689 2598 1.32251997 Root MSE = 1.1359
Adj R-squared = 0.0244
Residual 3350.74905 2597 1.29023837 R-squared = 0.0248
Model 85.1578406 1 85.1578406 Prob > F = 0.0000
F( 1, 2597) = 66.00
Source SS df MS Number of obs = 2599
. reg maritalq hinc
a. (4 points) Run a regression of maritalq on hinc with no control variable. Write the
estimated regression equation based on the Stata regression output. What is the
estimated slope of hinc? Interpret the estimated slope.
Answer
The estimated regression equation is;
MaritalQ=5.0074+0.1403( Hinc)

The estimated slope is 0.1403; this means that a unit increase in the husband’s income
would result to an increase in the marital quality by 0.1403. Similarly, a unit decrease
in the husband’s income would result to a decrease in the marital quality by 0.1403.
b. (5 points) State the null hypothesis and the alternative hypothesis which correspond to
the slope coefficient of hinc in the Stata regression table. Can you reject the null
hypothesis in favor of the alternative hypothesis at 5% significance level? Justify your
answer using three kinds of evidence, (1) confidence interval, (2) t statistics, and (3)
p-value.
Answer
The hypothesis is;
Null Hypothesis (H0): Slope is not significantly different from zero
Alternative Hypothesis (HA): Slope is significantly different from zero
From the results we reject the null hypothesis.
Justification using confidence interval;
The 95% confidence interval is between 0.1064 and 0.1742, this clearly shows that
zero is not within the interval hence the rejection of the null hypothesis at 5% level of
significance.
Justification using t statistics
The computed t-value is 8.12; this value is clearly greater than the critical t value
from the tables (t = 1.96). This means that the null hypothesis is rejected at 5% level
of significance.
Justification using p-value

The p-value is given as 0.000; this value is less than the α = 0.05; we therefore reject
the null hypothesis at 5% level of significance.
c. (4 points) How much did the husband of the woman whose pid is 24 earn per month
in 2007? Predict her marital quality based on her husband’s income and the estimated
regression line in Q4.a. What was her actual marital quality in 2007? Calculate
residual in her marital quality. (*For predicted values and residuals, refer to the last
two pages of lecture notes in Week 8.)
Answer
The husband earned 2,500 USD per month.
The estimated marital quality is;
MaritalQ=5.0074+0.1403(2.5)
MaritalQ=5.0074+0.35075=5.35815
The actual marital quality in 2007 was 5.
Residual=Actual value−Predicted value
Residual=5−5.35815=−0.35815
5. (15 points) Now, we consider the husband’s education in years as a control variable.
Output
a. (2 points) Explain theoretically or intuitively how the two conditions for omitted
variables might be satisfied for the husband’s years of education.
Answer
Condition 1: The control variable (husband’s education in years) is intuitively
thought to be correlated with the husband’s income. Husbands with higher education
levels (more years of education) tend to have higher income levels.

Condition 2: The control variable (husband’s education in years) affects the marital
quality. Higher education years might result to higher martial quality.
b. (2 point) Under the scenarios assumed in Q5.a, predict whether omitting the years of
education might make the estimated effect of the husband’s income upward or
downward biased. Briefly explain why.
Answer
Based on the above, omitting the years of education might make the estimated effect
of the husband’s income upward biased. This is based on the fact that years of
education is positively related with the marital quality.
c. (2 points) Now let’s run the regression with the additional control for the years of
education to the model in Q4.a. Run the regression and write the estimated regression
model.
Answer
_cons 4.29661 .1159383 37.06 0.000 4.069268 4.523951
hedy .0623724 .0090603 6.88 0.000 .0446061 .0801387
hinc .0827852 .0190244 4.35 0.000 .0454806 .1200897
maritalq Coef. Std. Err. t P>|t| [95% Conf. Interval]
Total 3418.67466 2584 1.32301651 Root MSE = 1.1262
Adj R-squared = 0.0414
Residual 3274.677 2582 1.2682715 R-squared = 0.0421
Model 143.99766 2 71.99883 Prob > F = 0.0000
F( 2, 2582) = 56.77
Source SS df MS Number of obs = 2585
. reg maritalq hinc hedy
The estimated regression equation is;
MaritalQ=4.2966+0.0828 ( Hinc ) + 0.0624( Herdy )
d. (2 points) Interpret the estimated slope coefficient of hinc.
Answer

The estimated slope is 0.0828; this means that a unit increase in the husband’s income
would result to an increase in the marital quality by 0.0828. Similarly, a unit decrease
in the husband’s income would result to a decrease in the marital quality by 0.0828.
e. (2 points) Are the two conditions for omitted variable bias associated with
educational attainment satisfied empirically? Answer with empirical evidence.
Answer
2660 2590 2666
0.0000 0.0000
hedy 0.1856 0.4339 1.0000
2599 2604
0.0000
hinc 0.1574 1.0000
2676
maritalq 1.0000
maritalq hinc hedy
. pwcorr maritalq hinc hedy, obs sig
Yes the two conditions are satisfied based on the empirical evidence. As can be seen
form the above table, there is positive relationship between husband’s education in
years and husband’s income (r = 0.4339). There is also positive relationship between
marital quality and husband’s education in years ( r = 0.1856)
f. (3 points) Based on your comparison of regressions in Q4.a and Q5.c, how does the
failure to control for husband’s education cause the estimated effect of the husband’s
income biased – upward, downward, or unbiased? Confirm the direction of the bias
using the empirical evidence from Q5.e.
Answer
Bias=0.1403−0.0828=0.0575
Bias=0.0575>0
Since the bias is greater than zero we can conclude that omitting the years of
education might make the estimated effect of the husband’s income upward biased.

g. (2 points) Which model, either the model in Q4.a or the model in Q5.c, do you prefer
and why?
Answer
I do prefer model in Q5.c. This is based on the fact that an increase in the value of
adjusted R-Squared is observed. In model Q4.a, the value of adjusted R-Squared was
0.0248 while for the model in Q5.c the value is 0.0414. This shows that a slightly
higher proportion of the variation in the dependent variable is explained in model
Q5.c as compared to model in Q4.a.
6. (10 points) Now, we consider the husband’s work hours as another control variable.
a. (2 points) Run the regression that additionally controls for variables related with the
husband’s work hours to the model you chose in Q5.g. Run the regression, and write
the estimated regression model.
Answer
_cons 4.209194 .1184698 35.53 0.000 3.976889 4.4415
hhour_5060 .1160036 .0719192 1.61 0.107 -.0250215 .2570287
hhour_4050 .2303237 .0557868 4.13 0.000 .1209323 .339715
hedy .0588287 .0090725 6.48 0.000 .0410385 .0766188
hinc .074213 .0190765 3.89 0.000 .0368061 .1116199
maritalq Coef. Std. Err. t P>|t| [95% Conf. Interval]
Total 3418.67466 2584 1.32301651 Root MSE = 1.1227
Adj R-squared = 0.0472
Residual 3252.19362 2580 1.26054016 R-squared = 0.0487
Model 166.481046 4 41.6202616 Prob > F = 0.0000
F( 4, 2580) = 33.02
Source SS df MS Number of obs = 2585
. reg maritalq hinc hedy hhour_4050 hhour_5060
The estimated regression equation is;
MaritalQ=4.2966+0.0742 ( Hinc ) +0.0588 ( Herdy ) +0.2303 ( hhou r 4050 ) +0.1160( hhou r5060 )
b. (2 points) Interpret each and every slope coefficient of the work hours.
Answer

The estimated slope for hincis 0.0742; this means that a unit increase in the husband’s
income would result to an increase in the marital quality by 0.0742. Similarly, a unit
decrease in the husband’s income would result to a decrease in the marital quality by
0.0742.
The estimated slope for herdy is 0.0588; this means that a unit increase in the
husband’s education in years would result to an increase in the marital quality by
0.0588. Similarly, a unit decrease in the husband’s education in years would result to
a decrease in the marital quality by 0.0588.
The estimated slope for hhour4050 is 0.2303; this means that husbands who work for
between 40 to 50 hours per week have higher marital quality by approximately
0.2303 as compared to the husbands who work 60 hours or more per week.
The estimated slope for hhour5060 is 0.1160; this means that husbands who work for
between 50 to 60 hours per week have higher marital quality by approximately
0.1160 as compared to the husbands who work 60 hours or more per week.
c. (4 points) Test a null hypothesis that the husband’s work hours do not matter to
marital quality against its alternative hypothesis. Using “β”s related to the husband’s
work hours, re-write the null hypothesis and write the alternative hypothesis. Can you
reject the null hypothesis at 1% significance level? Provide your evidence.
Answer
The null hypothesis that the husband’s work hours do not matter to marital quality
against its alternative hypothesis is rejected at 1% level of significance.
Using “β”s related to the husband’s work hours
H0 : β31=0

H A : β31 ≠ 0
Where β31 refers to the beta related to husbands work hours of between 40 to 50 hours
per week. The p-value related with the beta is 0.000 (a value less than 1% level of
significance), we thus reject the null hypothesis for this beta. And conclude that the
beta ( β31) related to husbands work hours of between 40 to 50 hours per week is
significantly different from zero at 1% level of significance.
H0 : β32=0
H A : β32 ≠ 0
Where β32 refers to the beta related to husbands work hours of between 50 to 60 hours
per week. The p-value related with the beta is 0.125 (a value greater than 1% level of
significance), we thus fail to reject the null hypothesis for this beta. And conclude that
the beta ( β32) related to husbands work hours of between 50 to 60 hours per week is
not significantly different from zero at 1% level of significance.
d. (2 points) What is the adjusted R squared of the regression in Q6.a? Interpret the
adjusted R squared.
Answer
The adjusted R squared of the regression in Q6.a is 0.0472; this implies that only
4.72% of the variation in the dependent variable (marital quality) is explained by the
three independent variables in the model.
7. (4 points) In Q3.d, we found some evidence of non-linearity between hinc and maritalq.
To relieve the concern about wrong functional forms, let’s examine the possibility of the
non-linear relationship for the regression in Q6.a.

a. (2 points) To do so, create logged income of the husband by taking log of hinc. Then
regress maritalq on the logged hinc and the control variables included in Q6.a.
Interpret the estimated slope coefficient for the husband’s income. (*This question is
related to our learning in Week 11. For preview, you can create logged variable1,
named as logvariable1 (or use whatever name you like), as below:
gen logvariable1 = ln(variable1)
//ln denotes natural log.
//“l” in ln is the lower case of “L” (NOT number one).
Answer
_cons 4.270958 .119513 35.74 0.000 4.036607 4.505309
hhour_5060 .1032547 .0719845 1.43 0.152 -.0378985 .244408
hhour_4050 .2117787 .0561387 3.77 0.000 .1016972 .3218602
hedy .0538514 .0092799 5.80 0.000 .0356547 .0720481
loghinc .2486177 .0539729 4.61 0.000 .1427832 .3544522
maritalq Coef. Std. Err. t P>|t| [95% Conf. Interval]
Total 3418.67466 2584 1.32301651 Root MSE = 1.1214
Adj R-squared = 0.0495
Residual 3244.5868 2580 1.25759178 R-squared = 0.0509
Model 174.087863 4 43.5219659 Prob > F = 0.0000
F( 4, 2580) = 34.61
Source SS df MS Number of obs = 2585
. reg maritalq loghinc hedy hhour_4050 hhour_5060
The estimated slope for loghincis 0.2486; since the coefficient is 0.2486, marital
quality will change by 0.002486 units when the husband’s income changes by 1%.
b. (2 points) Note the model in Q6.a and the model in Q7.a have no difference in terms
of variables used in the regressions. Instead, the models are different only in terms of
the functional form of hinc. Which model do you prefer, and why? Justify your
answer with evidence.
Answer
I do prefer model in Q7.a. This is based on the fact that an increase in the value of
adjusted R-Squared is observed. In model Q6.a, the value of adjusted R-Squared was

0.0487 while for the model in Q7.a the value is 0.0495. This shows that a slightly
higher proportion of the variation in the dependent variable is explained in model
Q7.a as compared to model in Q6.a. Implying that model in Q7.a is better than model
in Q6.a.
8. (10 points) Create a table which reports results from four regression models from Q4.a,
Q5.c, Q6.a, and Q7.a. To create the table, make it sure to read the attached “Guidelines
for Presenting Statistical Information” and refer to example regression tables in the
textbook (You do not have to report SER as the textbook tables do). Note this question is
about visual presentation of your statistical work. Pay your attention to DETAILS. In
addition, the table should look good when it gets printed. Hence, I suggest you edit the
final version of your table using MS Word (rather than other programs such as Excel) and
you check whether the table looks good when printed.
Answer
The following is the table that represents the results obtained in the above sections.
Table 1: Summary of Regression Analysis for Predicting Wives’ Marital Quality (N =
2682)
Model
1
Model
2
Model
3
Model
4
β β β β
Husband's income 0.1403* 0.0828* 0.0742*
Husband's education (in
years)
0.0624* 0.0588* 0.0539*
Number of working hours
Between 40 and 50 0.2303* 0.2118*
Between 50 and 60 0.116 0.1033
Log of husband's income 0.2486*
Constant 5.0074* 4.2966* 4.2092* 4.2710*

Adjusted R-Squared 0.0244 0.0421 0.0472 0.0495
* Significant at 1% level of significance
9. (16 points) Make your conclusion.
a. (2 points) Summarize your findings on the original policy question based on your
analysis above (i.e. Provide the statistical significance, sign, and size of the estimated
impact from the most preferred model).
Answer
This study sought to investigate the factors that affect the marital quality married
women aged between 20 and 64 years old. Results showed that the key factor that
influences the marital quality of women is their husband’s monthly income. Results
showed that a 1% change in the husband’s income would result to a 0.002486 units
change in the marital quality. Other factors that were found to influence the marital
quality were the husband’s education in years as well as the husband’s working hours
per week. In overall, even though the factors significantly influenced the marital
quality of women, the factors were found to have very little effect since only 4.95%
of the variation in the marital quality was explained by the factors.
b. (4 points) Based on your findings, provide two different kinds of policy
recommendations.

Answer
Based on the findings, the following policy recommendations would be ideal to
contain the situation.
 There is serious need to have work life balance for the men. Results showed
that women whose husband’s worked for longer hours a week tended to have
low marital quality as compared those women whose husband’s worked for
shorter hours a week. As such, there if therefore need to help come up with a
work life balance that would enable men spent better time with their wives.
 Need to encourage learning by the men. Results showed that women whose
husbands had higher number of education years had had better marital quality
as compared to those whose husband’s had lower education levels (in years).
This implies literacy levels tend to help improve marital quality.
c. (8 points) Assess your analysis in terms of internal validity.
Answer
The internal validity of the analysis is threatened by the following;
Omitted variable bias; as could be seen from the initial model, the analysis suffers
from omitted variable bias. This is true from even when checking the value of
adjusted R-Squared we found that only a very small proportion of the variation is
explained by the variables in the model. This clearly shows that other variables
outside the model that would have greatly influenced the dependent variable have
been omitted from the model.
Missing data could also introduce some bias in the results. It found that most data
were missing for the variable husband’s income. So it could be that there was

deliberate decision not to give information on income by the participants. This could
possibly result to bias as a result of missing data.
d. (2 points) Briefly discuss external validity of your analysis.
Answer
The study does not mention on the sampling procedure that was used. It is therefore
very difficult to conclude that the results are generalizable hence external validity of
the results is threatened.