Correlation and Regression Analysis in Statistics

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.