Linear Regression Analysis Report: Life Satisfaction vs. GDP

Desklib provides solved assignments and past papers to help students succeed.

LINEAR REGRESSION REPORT
1

Table of Contents
1. Purpose....................................................................................................................................3
2. Background.............................................................................................................................3
3. Method.....................................................................................................................................3
4. Results......................................................................................................................................4
5. Discussion................................................................................................................................7
6. Recommendations..................................................................................................................7
References.......................................................................................................................................9
2

1. Purpose
The main purpose of preparing the following report is to identify the nature and extent of
relationship that normally exists between the two given variables, namely, average life
satisfaction and annual GDP per capital of 35 different nations. Some widely used statistical
tools and techniques have been applied on these variables so as to take suitable and appropriate
decisions accordingly. All the statistical tools have been applied considering the purpose of the
research.
2. Background
In this report, two variables have been taken into consideration for the purpose of analysis and
decision-making. The only purpose is to take suitable decisions through decision-making. The
background of this research moves around the two variables (Shazmeen, et. al., 2013). These two
variables have been determined in accordance with nations or countries of the worlds. In other
words, the major nations or countries have revolved around the two variables, namely, ‘life
satisfaction score’ and ‘GDP per capita’. These two variables represent the position and
situations of the given nations and countries.
3. Method
There are different data source methods that are used to properly analyse and interpret the data.
A correct and meaningful interpretation is very essential and crucial for the decision making
purpose. In this particular research case study, ‘Continual data analysis’ has been used in the data
collection phase. Furthermore, the empirical method has been applied in the data collection and
analytical method (Ostertagová, et. al., 2014).
There are various significances of the empirical method. The main focus of empirical method is
to find out the empirical evidence or proof. However, there are certain limitations within which
empirical method is generally applied. For the betterment of outcome or result, it would be
profitable and beneficial to apply empirical method along with data analysis.
3

4. Results
Average life satisfaction
Mean 6.59
Standard Error 0.13
Median 6.70
Mode 7.50
Standard Deviation 0.75
Sample Variance 0.56
Kurtosis -1.10
Skewness -0.43
Range 2.30
Minimum 5.20
Maximum 7.50
Sum 230.70
Count 35.00
Annual GDP per capita
Mean 39011.51
Standard Error 2367.48
Median 37843.04
Mode #N/A
Standard Deviation 14006.21
Sample Variance 196174046.40
Kurtosis 2.81
Skewness 1.29
Range 69665.61
Minimum 17122.53
Maximum 86788.14
Sum 1365402.96
Count 35.00
Above two tables indicates the descriptive statistics of the given two variables. It can be
observed that the two countries, namely, Greece and Portugal have lowest average life
satisfaction scores of 5.2. Furthermore, no country has same average life expectancy score.
4

On the other hand, country ‘Mexico’ has the lowest annual GDP per capita and Luxembourg has
the highest GDP per capita.
Before applying the regression model, it is imperative to understand the fact that the GDP per
capita has been taken to be the independent variable and consequently the ‘average life
satisfaction’ has been assumed to be the dependent variable.
0 5 10 15 20 25 30 35 40
0.00
2.00
4.00
6.00
8.00
10.00
12.00
f(x) = NaN x + NaN
R² = 0 Relation between average life satisfaction and
annual GDP
Relation between average life
satisfaction and annual GDP
Linear (Relation between average
life satisfaction and annual GDP)
Linear (Relation between average
life satisfaction and annual GDP)
The above scatter diagram depicts between these two variables. It can be observed that there is a
fluctuating trend or movement in these two variables. Accordingly, it can be observed that at
some points, there is an annual GDP per capita with the increase in average life satisfaction. On
the other hand, there are some points where annual GDP per capita has decreased with the
increase in life satisfaction (Mrkvicka, et. al., 2016). In other words, there is a positive
relationship between these two variables at some points. On the other words, there is a negative
relationship between the given set of variables.
5

y = 0.071x + 5.306
R² = 0.963
Substituting the value of x, the value of y can easily be determined or vice versa.
The above regression equation explains the linear relationship between the two given variables.
It can be observed that coefficient of determination, R² is 0.963. It is used to explain the amount
and volume of variance in dependent variables (here, GDP per capita) and the independent
variable (here, average life satisfaction). This regression equation will help to predict the annual
GDP per capita considering or on basis of the average life satisfaction (Lai and Kelley, 2012).
There are certain parameters on which the regression analysis can be measured or evaluated. In
other words, assessing the fit of regression models can be done on the basis of which it is
evaluated whether regression model provides a good fit or not. Considering the nature and extent
of relationship, it can be observed that the above mentioned regression model provide a good fit.
In addition, it can be concluded that there is a strong statistical relationship or association
between or within the annual GDP and average life satisfaction. This can be clearly observed
from the coefficient of determination or R2. In other words, it can be said that the variable
‘annual GDP’ can be predicted from or through the assistance of variable ‘average life
satisfaction score’.
Ignoring the three countries namely, Luxembourg, Ireland and Norway, the required regression
model will be as follow:
SUMMARY OUTPUT
Regression
Statistics
Multiple R 0.70
R Square 0.50
Adjusted R
Square
0.48
Standard Error 0.55
Observations 32.00
6

ANOVA
df SS MS F Significa
nce F
Regression
1.00 8.79 8.7
9
29.5
4
0.00
Residual
30.00 8.93 0.3
0
Total 31.00 17.72
Coeffic
ients
Standard
Error
t
Sta
t
P-
valu
e
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept
4.56 0.38 12.
06
0.00 3.78 5.33 3.78 5.33
Annual GDP
per capita
0.00 0.00 5.4
3
0.00 0.00 0.00 0.00 0.00
It can be clearly observed that after eliminating the data pertaining to three countries, it will
create a huge difference. As such, when the intercept of all the 35 countries comes to be 5.37, the
intercept coefficient ignoring these three major countries will be 4.56.
5. Discussion
Several major interpretations and outcomes have been determined through the application of
major and widely statistical tools and techniques. These outcomes need to be carefully applied so
that it can help in decision making process or phase. A complete understanding of nature and
characteristics of the data will help the governmental organizations as well as private research
associations. Necessary precaution has been taken by the each and every member of the research
team (Kim, 2015).
6. Recommendations
It is advisable to carefully apply the outcome derived from the analytical phase of the data
collected. There are certain limitations as well as assumptions normally associated with the
decision making process. It is expected from the reader or user of the report that he is fully
conversant or aware with these assumptions. For the betterment of outcome, certain specific
assumptions need to be mentioned by the researcher or the research team.
7

8

References
 Kim, T.K., 2015. T test as a parametric statistic. Korean journal of anesthesiology, 68(6),
pp.540-546.
 Lai, K. and Kelley, K., 2012. Accuracy in parameter estimation for ANCOVA and ANOVA
contrasts: Sample size planning via narrow confidence intervals. British Journal of Mathematical
and Statistical Psychology, 65(2), pp.350-370.
 Mrkvicka, T., Hahn, U. and Myllymaki, M., 2016. A one-way ANOVA test for functional data
with graphical interpretation. Functional ANOVA test.
 Ostertagová, E., Ostertag, O. and Kováč, J., 2014. Methodology and application of the kruskal-
wallis test. In Applied Mechanics and Materials, 611, 115-120.
 Shazmeen, S.F., Baig, M.M.A. and Pawar, M.R., 2013. Regression Analysis and Statistical
Approach on Socio-Economic Data. International Journal of Advanced Computer Research,
3(3), p.347.
9