Quantitative Methodology: Correlation Coefficient, Regression Model and Assumptions

This study focuses on the use of Spearman correlation coefficient in the presence of nominal variables, evaluation of regression model and assumptions related to it. The linear regression model is statistically significant and assumptions like normality, linearity and homoscedasticity of residuals are met. The study is subject to Quantitative Methodology with no specific course code, course name or college/university mentioned.

The Quantitative
methodology

Table of Contents
MAIN BODY...................................................................................................................................3
Identify the correlation coefficient used in the table provided...............................................3
Critically evaluate if the selected correlation is appropriate along with reasons...................3
Evaluate the regression model and discuss the assumptions related to it...............................3
REFERENCES................................................................................................................................6

MAIN BODY
The first two answers replied are correct as per the knowledge.
Identify the correlation coefficient used in the table provided.
Spearman Correlation coefficient is used in obtaining the results.
Critically evaluate if the selected correlation is appropriate along with reasons.
In this data, Spearman correlation coefficient is used even in the presence of nominal
variables such as male, education, knows other entrepreneurs. It is very much known that this
Method of calculating coefficient correlation is not used for nominal variables and it is never
recommended to use this model in presence of both nominal as well as ordinal variables. But the
study is about the young firms of number of countries and the presence of nominal variables does
not put any impact on the results driven from the coefficient. The focus is mainly on creating a
relation among the two available variables such as intellectual property held by persons having
specific level of education, the GDP growth rate in relation to the entrepreneur employment
growth aspiration. But there are several other models like Pearson which can be used here for
receiving more appropriate results.
Yes, the nominal variables are the control variables due to which they are included in the
study. The gender current level of employment, previous entrepreneurial experience all are
control variables. Along with this, capital intensity and optimum size of firm are also controlled
by the researchers. They all holds the capacity to influence the results driven from tables and are
thus required to be controlled (Parker, 2009).
Evaluate the regression model and discuss the assumptions related to it.
Multiple linear regression is used in this table. This is a statistical tool that makes use of
various explanatory variables which can help in predicting the outcome of response variable. It
helps in estimating that how a dependent variable change with a change occurring in an
independent variable. Researchers makes use of dummy coding for variables like age, gender,
bus angel and many more in the form of 0 and 1 in order to enable them to be used in a single
regression equation. Moreover, it makes easy for the software to analyse the data present in
binary function. Also., it makes it easy to interpret and calculate ratios.
Multilevel modelling has been used for cross country, cross-time and cross-individual
data base. This is because it allows a control over the clusteration of data set within a country

and in a country year sub sample (Rabe-Hesketh, Skrondal, Pickles, 2005).This is because in
absence of this modelling the results driven can be biased which would lead to wrong decisions.
Yes the linear regression model is statistically significant because it predicts the value of one
variable on the basis of other value.
A simple linear regression equation describes the relation among the different variables
by making a line of the provided data. It is straight line and the values are presented near about it
showing the accurate variation. Whereas multiple linear regression equation represents the value
of one variable on the basis of many variables. The desired result is the dependent variable in this
model.
# Regression Model’s Assumptions Are they met?
1 One dependent continuous variable. YES, employment growth aspirations
2 At least one independent variable. One
of the independent variables should be
continuous.
YES, government size
3 Sample size. YES, 8160
4 Normality. Each continuous variable
should be normally distributed.
No, because there is lot of variation between
mean and standard deviation.
5 Outliers. Linear regression (like
Pearson’s correlation coefficient, which
draws on normality or linearity of data)
is sensitive to outliers, especially
extreme values.
Note: If significant outliers (e.g.,
extreme values/observations) are present,
they should be removed or converted
(e.g., logarithmic transformation) before
running the linear regression model.
YES, There were 171 outliers in the
observations that were eliminated (Autio,
Acs, 2010).
6 Independence of observations. The
residuals should be independent.
Otherwise, there are referred to as
correlated.
Note: We check the independence of
observations using the Durbin-Watson
statistic.
No, all the variables are not independent.
For example, corruption is correlated with
GDP per capital
7 Multicollinearity. High correlations (e.g.,
𝑟≥0.80) between predictors make a
regression model very difficult to
interpret.
Note: We should construct a correlation
matrix (table) before running a linear
YES, the data is highly correlated. The
corruption is highly correlated (Djankov,
and et. al., 2002).

# Regression Model’s Assumptions Are they met?
regression model to identify independent
variables with significantly high
correlations.
Note: Multicollinearity can be detected
in SPSS with the Tolerance and VIF
(Variance Inflation Factor) statistics.
8 Normality, Linearity, and
Homoscedasticity of residuals (𝜺).
Critical assumptions for obtaining valid
results from regression models are:
a. The residuals are normally distributed
(normality).
b. The relationship of the residuals with
the predicted or estimated values of the
dependent variable (𝑦̂ ) is linear
(linearity).
c. The variance in the residuals is
homogeneous across the full range of
predicted values (homoscedasticity,
which is also known as homogeneity of
variance).
a. YES, it is clear in the graph that the
values are normally distributed.
b. YES, this is because the expected values
are estimated from the actual figures of
previous figure.
c. YES, there is a homogeneity in the
values.

REFERENCES
Books and Journal
Autio, E., Acs, Z., 2010. Intellectual property protection and the formation of entrepreneurial
growth aspirations. Strategic Entrepreneurship Journal 4 (3), 234–251.
Djankov, S. and et. al., 2002. The regulation of entry. Quarterly Journal of Economics CXVII 1,
1–36.
Parker, S.C., 2009. The Economics of Entrepreneurship. Cambridge University Press,
Cambridge, UK.
Rabe-Hesketh, S., Skrondal, A., Pickles, A., 2005. Maximum likelihood estimation of limited
and discrete dependent variable models with nested random. Journal of Econometrics
128 (2). 301–323
(Qasim, Amin and i, Aarthi and Abhinaya, 2017)(Xu and Doi, 2018)