Managerial Economics Problem Set 3: Correlation and Regression

This assignment addresses key concepts in Managerial Economics, specifically focusing on Problem Set 3. The solution begins by explaining the difference between correlation and causation, providing an illustrative example of ice cream sales and drowning to highlight that correlation does not necessarily imply causation. It then delves into how regression analysis attempts to address this issue. The assignment also explains the meaning and importance of statistical significance of an independent variable, emphasizing its role in hypothesis testing and research outcomes. Finally, it discusses the benefits of including multiple independent variables in a regression model, highlighting how this enhances the richness and credibility of the analysis. The solution includes references to support the explanations provided.

1.
Correlation either positively correlated or negatively correlated and its correlation
varies between +1 to -1. It shows relationship between two variables and its
degree of relationship. When two variables are positively correlated, it is observed
and established that if one variable goes up, second variable will also go up,
simultaneously. It indicates that change in one variable will lead to change in
second variable as well. To know it even better, it needs further explanation, the
change in one variable lead to change in second variable together, it has four
possible reasons:
1. Y is changing because of X
2. X is changing because of Y
3. Or could be third variable, that is, Z is causing both of them to alter
4. It is purely by chance, there is, in fact, no real relationship exists between these
two variables
As you have been already observe above that there can be multiple possibilities
for change in one variable lead to change in another variable, it cannot solely
attributed to the fact that X is causing Y to change or Y is causing X to change.
Further, disengagement is not possible in these four possibilities, in most of the
cases of this kind.

Example of Correlation but no causal relationship exists. This example is related
to the correlation between ice cream sales and drowning. Correlation can be found
between ice cream sales and drowning, but, how far there is real correlation needs
further examination of given variable and presence of may be other independent
variable. One can draw conclusion from this that there is some correlation
between these two variables, means ice cream sales increases the drowning
accident, which sounds very illogical for any individual, as how ice cream sales
would increase the drowning accident. Obviously, it is not the case, upon
scrutinizing the data, it promptly found that a third variable, that is, time of
year/temperature, is also present there which causing these two things to happen,
that is, the ice cream sales and the drowning accidents.
As we all know that regression is all about analysis or explanation of impact of
one factor on another factor, it will be pertinent to keep in mind the relevant
proverb: ‘Does Causation occur because of correlation?’ Correlation is not
causation’, is critical to say here is why: one can easily draw conclusion that
correlation between two factors, here it is rain and monthly sales does exist and it
may also authenticate the regression analysis. However, it cannot say that because
of rain because of rain sales of umbrellas increased. Umbrellas sale can also be
increase due to scorching sun heat. It is not that much easy to establish the
relationship between cause and effect.
2.

It is applied to see the significance of data and its relationship among various
variable. To say in other words it is chances of a relationship between two or
more than two variables are caused by something other than mere probability or
chance. It is used by statistician to admit or disapprove the null hypothesis, which
hypothesizes that there is absence of relationship among measured variables. It is
one of the very important aspects for statistical analysis and also for performing
research in social science or science or in any other subject. Hypothesis is one of
the major aspects of any research study, this Statistical significance play important
in determining result of any research study.
3.
If there is multiple variables are available in regression analysis it enhances the
credibility of the regression analysis and authenticity of report/ or research study,
because, it is based on more than one independent variables. When some
prediction are made based on only one independent variable it is not that much
authentic, but if independent variable is more than one it enhances the credibility
of prediction by regression analysis for any projection. When only one
independent variable is applied for prediction it can cause error in prediction and
prediction is remain questionable by the expert. Once, independent variable is
increased to two or even more than two it’s automatically enhances the predicted
value’s importance for any study, that is why its importance in any study whether
it is academic or corporate study or financial sector study. Independent variable’s

larger presence in research study is very important, if it is more than two it will
benefit the study
References
Statistical testing of significance | ESS EduNet. (2019). Retrieved 13 September 2019, from
http://essedunet.nsd.uib.no/cms/topics/regression/4/2.html

Man, F. (2017). When can correlation equal causation?. Retrieved 13 September 2019, from
https://thelogicofscience.com/2017/10/03/when-can-correlation-equal-causation/