Linear Regression Analysis Report: Life Satisfaction vs. GDP

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LINEAR REGRESSION REPORT
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Table of Contents
1. Purpose....................................................................................................................................3
2. Background.............................................................................................................................3
3. Method.....................................................................................................................................3
4. Results......................................................................................................................................4
5. Discussion................................................................................................................................7
6. Recommendations..................................................................................................................7
References.......................................................................................................................................9
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1. Purpose
The whole and sole purpose of preparing this particular report is to gain an in depth
understanding of these two variables. Further the report provides for the relationship that exists
between the two variables. The two variables in this regar5d majorly include average life
satisfaction and annual GDP per capital of 35 nations. To elaborate a greater understanding
series of the statistical tools and techniques have been used so as to enable the authorities to
make suitable and appropriate decision. All the tools have been applied taking into consideration
the objectives of the research.
2. Background
For the analysis and better decision making the report work takes into consideration the two
variables. The main objective of the research work is to ensure suitable decision making with
respect to the working patterns. Foe elaborated and better understanding the research work takes
into parameter two variables (Shazmeen, et. al., 2013). The variables have been selected in
accordance of the terms of different nations. As such itcan be said that the two variables have
beenselected taking into the compliance requirement of different nation that includes ‘life
satisfaction score’ and ‘GDP per capita’. The two variables provides for a clear picture of varied
situation prevailing in different nations.
3. Method
For the effective analysis and interpretation of the data there are different methods that can be
used for the assortment of the data. The selection of the suitable method is very crucial as it will
assist in the attainment of the better decisions making with respect to the working patterns of the
current as well upcoming activities. For the current researchwork, ‘Continual data analysis’ has
been used for the gathering of the useful data. In addition, empirical method has been used as an
analytical tool.
With the use of the empirical method there are varied factors of significance that can be attained
such as the method provides for the suitable evidence for proof that can be used for the further
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activities.As, such it is recommended that to attain suitable outcome empirical method along
with the analysis of the data must be applied so as to have better command
4. Outcome
Life satisfaction score of 35 countries
Mean 6.59
Standard Error 0.13
Median 6.70
Mode 7.50
Standard Deviation 0.75
Sample Variance 0.56
Range 2.30
Minimum 5.20
Maximum 7.50
Annual GDP per capita of 35 countries
Mean 39011.51
Standard Error 2367.48
Median 37843.04
Mode #N/A
Standard Deviation 14006.21
Sample Variance 196174046.40
Range 69665.61
Minimum 17122.53
Maximum 86788.14
The concerned table depicts on the descriptivestatistics of the two variables. With the analysis of
the table it has been observed that the two countries that include Greece and Portugal have the
least average life satisfaction that scores to 5.2. In addition, it has been observed no other country
stands on such score. Further provided, with the analysis it has been addressed that ‘Mexico’ has
the lowest annual GDP per capita and Luxembourg has the highest GDP per capita.
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Previously, the application of the regression model it was difficult to understand that GDP per
capita income is an independent variable and also ‘average life satisfaction’ is a 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)
With the above scatter diagram it has been analyzed that there is a fluctuating trend among the
two variables. As such it can be observed that in some situations there is enhancement in the
annual GDP per capitawith the enhancement in the average life satisfaction. On the contrary,
there are situation where the annual gross domestic product is decreasing while there is an
increase in the average life satisfaction (Mills & Tosic, 2011). As such it can be concluded
thatthere is a positive relation of the two variables at some points while at some points they have
negative relation.
y = 0.071x + 5.306
R² = 0.963
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While replacing the value of x, the value of y can be easily determined or computed. It can be
clearly observed that the Coefficient of determination is high enough indicative to prove that
there is a higher relationship between these two variables. Thus, coefficient of determination
between the two given variables is 0.963, i.e., life satisfaction score and annual GDP.
Regression table of give
two variables
Regression
Statistics
Multiple R 0.70
R Square 0.50
Adjusted R
Square
0.48
Standard Error 0.55
Observations 32.00
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
Coeffici
ents
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
The above regression analysis table depicts or indicates the intercept coefficient taking the GDP
coefficient as dependent variable while life expectancy scores as the independent variable (Sow,
2014).
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5. Discussion
Throughout the report, these two variables have been discussed in detail. Such type of discussion
is crucial and of utmost importance before arriving at any conclusion. As such, it becomes
essential to have complete understanding regarding the variables.
6. Recommendations
Several recommendations and useful interpretations have been derived there from so that
necessary actions can be taken accordingly (Sow, 2014). There are several assumptions
associated with the statistical tools and techniques performed that have thoroughly discussed at
appropriate places in the report.
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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.
 Mills, R., & Tosic, D. 2011. Regression Analysis Applications in Litigation. ERS Group.
 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.
 Sow, M. T. 2014. Using ANOVA to examine the relationship between safety & security and
human development. Journal of International Business and Economics, 2(4), 101-106.
 Winter, B. 2015. The F-distribution and the basic principle behind ANOVAs.
Http://www.Bodowinter.Com, 1-18.
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