Business Statistics Project: Sovereign Bonds and Foreign Capital

This project analyzes the determinants of the cost of foreign capital for sovereign borrowers using a provided dataset. The analysis begins with descriptive statistics, including mean, standard error, median, mode, standard deviation, variance, kurtosis, skewness, range, minimum, maximum, and count for several variables (Interest 2019, democratic, Freedom of press, property rights, and default). Boxplots are used to identify outliers. Correlation between the variables are analyzed. The project then formulates and tests several hypotheses regarding the relationship between foreign capital and other variables, using simple and multiple linear regression models. The results of the regression analyses are presented, including coefficients, standard errors, t-stats, p-values, and ANOVA tables. Independent-sample t-tests are conducted to assess differences in means of interest 2019 between default and non-default statuses for other variables. Finally, conclusions are drawn regarding the relationships between the variables and the implications for the cost of foreign capital. The project includes detailed statistical outputs and interpretations.

Applied Business Statistics
Statistics
Student name:
Tutor name:
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Applied Business Statistics
QUESTION ONE
Descriptive statistics for dependent and independent variables
Interest
2019
democrati
c
Freedom of
press
property
rights default
Mean 8.01 Mean 3.49 Mean 36.31 Mean 4.20 Mean 0.47
Std error 1.32 Std error 0.43 Std error 1.99 Std error 0.28 Std error 0.07
Median 5.92 Median 3.00 Median 31.16 Median 4.00 Median 0.00
Mode 3.00 Mode 0.00 Mode 43.13 Mode 4.00 Mode 0.00
Std dev 9.26 Std dev 3.00 Std dev 13.95 Std dev 1.97 Std dev 0.50
Variance
85.7
3 Variance 8.98 Variance
194.6
6 Variance 3.87 Variance 0.25
Kurtosis
20.7
0 Kurtosis -0.72 Kurtosis 1.18 Kurtosis -1.14 Kurtosis -2.07
Skewness 3.96 Skewness 0.62 Skewness 0.95 Skewness -0.18
Skewnes
s 0.13
Range
60.0
0 Range
10.0
0 Range 66.96 Range 6.00 Range 1.00
Minimum 0.00 Minimum 0.00 Minimum 11.33 Minimum 1.00
Minimu
m 0.00
Maximum
60.0
0 Maximum
10.0
0 Maximum 78.29 Maximum 7.00
Maximu
m 1.00
Count
49.0
0 Count
49.0
0 Count 49.00 Count
49.0
0 Count
49.0
0
Table 1
The table above is of summary statistics of all the variables. The mean interest 2019 is 8.01,
democratic is 3.49, freedom of press is 36.31 and property rights is 4.2.
Boxplot
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Applied Business Statistics
defaultproperty rightsFreedom of pressdemocraticInterest 2019
80
70
60
50
40
30
20
10
0
Data
Boxplot of Interest 201, democratic, Freedom of p, property rig, ...
Figure 1
The boxplot above shows the distribution of various variables as shown. It was employed to
determine the anomalies in data such as outliers. It can be observed that there were outliers in the
variables “interest 2019” and “freedom of press”.
Correlation between the variables
Interest
2019 democratic
Freedom of
press
property
rights default
Interest 2019 1
democratic 0.090 1.000
Freedom of press 0.041 -0.347 1.000
property rights -0.144 0.415 -0.632 1.000
default 0.210 -0.015 -0.038 0.006 1
Table 2
QUESTION TWO
Theoretical model
Hypotheses
Hypothesis 1
H0: There is no relationship between cost of foreign capital and democratic.
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Applied Business Statistics
H1: There is a significant relationship between cost of foreign capital and democratic.
The level of significance = 0.05
Hypothesis 2
H0: There is no relationship between cost of foreign capital and property rights.
H1: There is a significant relationship between cost of foreign capital and property rights.
The level of significance = 0.05
Hypothesis 3
H0: There is no relationship between cost of foreign capital and default.
H1: There is a significant relationship between cost of foreign capital and default.
The level of significance = 0.05
Hypothesis 3
H0: There is no relationship between cost of foreign capital and freedom of press.
H1: There is a significant relationship between cost of foreign capital and freedom of press.
The level of significance = 0.05
QUESTION THREE
Simple regression equation between the independent variable and the 4 dependent
variables
a. Simple linear regression between foreign capital and democratic
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Applied Business Statistics
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.090158758
R Square 0.008128602
Adjusted R Square -0.01297505
Standard Error 9.318970743
Observations 49
ANOVA
df SS MS F Significance F
Regression 1 33.44985401 33.44985 0.385175 0.53784455
Residual 47 4081.631139 86.84322
Total 48 4115.080993
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 7.034876168 2.055481399 3.422496 0.001295 2.899780963 11.1699714
democratic 0.278557682 0.448834235 0.620625 0.537845 -0.62438033 1.1814957
Table 3
Foreign capital=0.28 ( democr atic )+7.03
b. Simple linear regression between foreign capital and property rights
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.1439967
R Square 0.020735
Adjusted R Square -0.0001004
Standard Error 9.2595605
Observations 49
ANOVA
df SS MS F Significance F
Regression 1 85.3263783 85.32638 0.995182 0.32358762
Residual 47 4029.75461 85.73946
Total 48 4115.08099
CoefficientsStandard Error t Stat P-value Lower 95% Upper 95%
Intercept 10.854605 3.14623665 3.450028 0.001194 4.52519368 17.18402
property rights -0.6773807 0.67901842 -0.99759 0.323588 -2.0433896 0.688628
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Applied Business Statistics
Table 4
Foreign capital=−0.68 ( property rights ) +10.85
c. Simple linear regression between foreign capital and freedom of press
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.040817326
R Square 0.001666054
Adjusted R Square -0.01957509
Standard Error 9.349280374
Observations 49
ANOVA
df SS MS F Significance F
Regression 1 6.855947574 6.855948 0.078435 0.78065823
Residual 47 4108.225045 87.40904
Total 48 4115.080993
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 7.023401298 3.75692363 1.869455 0.067797 -0.5345542 14.5813568
Freedom of press 0.027087753 0.096720252 0.280063 0.780658 -0.1674883 0.2216638
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Applied Business Statistics
Table 5
Foreign capital=0.027 ( freedomof press ) +7.02
d. Simple linear regression between foreign capital and default
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.21004915
R Square 0.04412064
Adjusted R Square 0.02378279
Standard Error 9.14832966
Observations 49
ANOVA
df SS MS F Significance F
Regression 1 181.5600222 181.56 2.169385 0.147448343
Residual 47 3933.520971 83.69194
Total 48 4115.080993
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 6.19637992 1.794135056 3.453686 0.001181 2.587045742 9.805714099
default 3.85707036 2.618721139 1.472883 0.147448 -1.411117047 9.125257772
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Applied Business Statistics
Table 6
Foreign capital=3.86 ( default )+ 6.2
e. Multiple linear regression between foreign capital and the independent variables
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Applied Business Statistics
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.3082286
R Square 0.0950049
Adjusted R Square 0.0127326
Standard Error 9.1999607
Observations 49
ANOVA
df SS MS F Significance F
Regression 4 390.9528486 97.73821 1.154762 0.343709
Residual 44 3724.128144 84.63928
Total 48 4115.080993
CoefficientsStandard Error t Stat P-value Lower 95%Upper 95%
Intercept 10.274643 7.71582472 1.331632 0.189839 -5.27558 25.82487
democratic 0.5586584 0.49071705 1.138453 0.261092 -0.43032 1.547634
Freedom of press -0.030656 0.123850807 -0.24752 0.805657 -0.28026 0.218949
property rights -1.174144 0.904109973 -1.29867 0.200821 -2.99626 0.64797
default 3.9030748 2.636826038 1.480217 0.145941 -1.4111 9.217248
Table 7
Foreign capital=0.56 ( democratic ) −0.03 ( freedomof press ) −0.03 ( property rights ) +3.9 ( default ) +10.27
NUMBER FOUR
Independent-sample t-test
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Applied Business Statistics
a. Test for the difference in means of interest 2019 between default and non-default
Independent Samples Test
Levene's Test for
Equality of
Variances
t-test for Equality of Means
F Sig. t df Sig. (2-
tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower Upper
interest_2
019
Equal variances
assumed
2.583 .115 -1.473 47 .147 -3.85694 2.61872 -9.12512 1.41124
Equal variances
not assumed
-1.409 28.630 .170 -3.85694 2.73712 -9.45813 1.74425
Table 8
The p-value computed is 0.115. This is greater than the alpha value which is 0.05. This means
that the null hypothesis is not rejected. It is concluded that there is no difference in mean interest
2019 between defaults and non-defaults.
b. Test for the difference in means of interest 2019 between default and democratic
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Applied Business Statistics
Independent Samples Test
Levene's Test for
Equality of
Variances
t-test for Equality of Means
F Sig. t df Sig. (2-
tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower Upper
democratic
Equal variances
assumed
.191 .664 .100 47 .921 .08647 .86686 -1.65742 1.83036
Equal variances not
assumed
.101 46.933 .920 .08647 .85813 -1.63993 1.81288
Table 9
The p-value computed is 0.664. This is greater than the alpha value which is 0.05. This means
that the null hypothesis is not rejected. It is concluded that there is no difference in mean
“democratic” between defaults and non-defaults.
c. Test for the difference in means of interest 2019 between default and freedom of
press
Independent Samples Test
Levene's Test for
Equality of
Variances
t-test for Equality of Means
F Sig. t df Sig. (2-
tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower Upper
Freedom of
press
Equal variances
assumed
2.105 .154 .257 47 .799 1.03528 4.03310 -7.07827 9.14883
Equal variances
not assumed
.263 44.17
1
.794 1.03528 3.94079 -6.90599 8.97655
Table 10
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Applied Business Statistics
The p-value computed is 0.154. This is greater than the alpha value which is 0.05. This means
that the null hypothesis is not rejected. It is concluded that there is no difference in mean
“freedom of press” between defaults and non-defaults.
d. Test for the difference in means of interest 2019 between default and property rights
Independent Samples Test
Levene's Test
for Equality of
Variances
t-test for Equality of Means
F Sig. t df Sig. (2-
tailed)
Mean
Difference
Std. Error
Difference
95% Confidence Interval
of the Difference
Lower Upper
Property
rights
Equal variances
assumed
.771 .384 -.044 47 .965 -.02508 .56937 -1.17052 1.12035
Equal variances
not assumed
-.044 45.215 .965 -.02508 .57201 -1.17702 1.12685
Table 11
The p-value computed is 0.384. This is greater than the alpha value which is 0.05. This means
that the null hypothesis is not rejected. It is concluded that there is no difference in mean
“property rights” between defaults and non-defaults.
Conclusions
From the analysis of the data, several conclusions could be made. First, it can be concluded that
there is no significant difference in each variable when it comes to default and non-default
statuses. Not much anomalies were discovered as data was generally consistent save for a few
cases of outliers. Among all the explanatory variables, it was observed that foreign capital was
very sensitive to default status than other variables. This is explained by the largest coefficient
compared to the other variables.
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