We'll understand the difference between correlation and regression and discuss it.
1 - what is
correlation
2 - types
of correlation.
3 - positive
and negative correlation
4 - what is
regression
5 - lines
of regression
6 - simple
regression model
1 - What is Correlation
A correlation
is a statistical relationship between two entities,
it measures
the extent to which the two variables are linearly related in simple words,
it is a
measurement of strength of association between the two variables,
for example,
an increase
in the price of commodity is always accompanied by decrease in demand the value
of the correlation always lies between minus one to plus one
2 - Types of Correlation
There are
mainly three categories of correlation,
the first one
is positive and negative correlation,
the second
one is linear correlation and non-linear correlation and,
the third
bone is simple multiple and partial correlation.
3 - Positive and Negative Correlation
A positive
correlation means that a linear relationship is positive and the two variables
increases or decreases in the same direction as you can see from the graph.
An example,
Can be as
the number of trees cut down increases the probability of soil erosion also
increases.
A negative correlation is just the opposite the
relationship line has a negative slope as you can see from the graph and the
variables changes in the opposite direction,
that is one
variable decreases while the other increases to understand.
An example,
can be if a
car decreases the speed the time taken to reach the destination increases to
know more about the types of correlation.
4
- What is Regression
Regression
analysis like most multivariate statistics,
allows you to infer that there's arelationship.between two
or further variables,
these
relationships are seldom exact because,
there is a
variation caused by many variables not just the variables being studied.
in
regression analysis there are two types of variable,
Dependent variable
and,
Independent
variable.
Discuss
what the both variable represents a dependent variable is a variable whose
value is influenced or to be predicted.
Dependent
variable is often
denoted by y and is also known as a predicted variable.
Independent
variable which is denoted
by x is a variable which influences the value or is used for prediction, the
independent variable is also known as a predictor variable
5 - Line of Regression
the
regrqession line is a line which is used to describe the geste of a set of
data,
in other
words it gives the best trend of the given data regression lines are useful in
forecasting procedures,
its purpose
is to describe the interrelationship between the dependent variable and
independent variable.
the
regression equation of y and x describes the change in the value of y for given
changes in the value of x and vice versa.
in the
regression line equation x and y are the variables of interest in our data with
y the unknown or dependent variable and x the known or the independent variable
Discuss the
two key terms in this graph,
Slope
Slope is
the ratio of the vertical & horizontal distances b/w the 2 points on a line,
you can see
y-intercept which is the coordinate of the point at which the curve intersects
an axis there are some assumptions.
we take to
create the regression model,
first one
is the dependent variable is assumed to be normally distributed,
the values
of the dependent variable are statistically independent,
this means
that when we select the sample of a particular x it does not depend on any
other value of y,
third one
is error values of statistically independent.
Discuss a
simple regression model
A simple
regression model is used to depict a relationship between variables,
which are
commensurable to eachother.meaning the dependent variable increases decreases
with the independent variable.
the
equation of a simple regression model is y is equal to b naught plus b 1 x plus
e,
where y is
dependent variable x is independent variable b naught and b 1
represents
y intercept and the slope of the line respectively and e is the error variable
now let's
move on to excel to calculate the regression coefficient of a given data we are
on our excel workbook in front of us we have the data of temperature of the day
and sales of the ice cream on that day,
Try to
understand the regression analysis and summary output using this data
so the
first step is to go to the data tab and select data analysis,
then select
regression and click ok
we'll get
this table select the y range as ice cream sales,
this y
range is predictable variable also called as dependent variable for the input x
range,
select the
temperature in degree celsius.
this is the
explanatory variable also called as independent variable,
one thing
you should keep in mind is that both the x and y column must be adjacent to
each other,
we have the
label so we'll check the label and,
we'll
select the output range from g5
check the
residuals and click ok excel produces the following output
let's
analyze some key data
we got the
ask value to be 0.9676 which is very good,
this shows
that 96 percent of the variation in ice cream sales is explained by the
temperature of the day closer to the one the better the regression line fits
the data.
now let's
move little more and analyze
this
coefficient.
if you look
at the coefficient you will get the equation of the regression line in our case
it is minus
176.33 plus 27.68 into temperature of the day substituting the temperature of
the day for any given day we can find the sales of the ice cream
with our
discussion,
we can
conclude that there is a big difference between the correlation and regression,
although these
are studied together correlation is used to study whether the variables under
study are correlated,
whereas regression
is used to establish the functional relationship between the two variables,
the
equation of the regression line is a form y is equal to f x plus c,
correlation
is used to establish the strength of the association between the two variables
that are being studied,
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