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Correlation and Regression Analysis: Simplest Way To Learn With Examples | Get Complete Clarity - YouTube
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Hello Friends,
In the last video of Scatter plot, we had
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seen how to detect, relationship between 02
or more variables, by using scatter plot and
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looking at the trend of scatter plot.
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But only obvious relationships can be detect
easily, by looking at the graph.
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In some cases, it is not possible to judge
the relationship between 02 variables, only
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looking at the graph.
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But the good thing is, we can comment about
the relationship between these variables using
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statistics.
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Yes, I am going to explain the use of statistics,
in determination of relationships between
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these variables, as well as to predict the
response of one variable, if we know the value
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of another variable.
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So let’s begin……
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Correlation:
The term correlation, is a combination of
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two words ‘Co’ (together) and relation
(connection) between two quantities.
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Correlation is when, at the time of study
of two variables, a unit change in one variable,
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is reacted by an equivalent change in another
variable, direct or indirect.
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Or else, the variables are said to be uncorrelated,
when the movement in one variable, does not
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show any movement in another variable, in
a specific direction.
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It is a statistical technique, which represents
the strength of the connection, between pairs
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of variables.
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Correlation can be positive or negative.
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When the two variables move in the same direction,
i.e. an increase in one variable, will result
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in the corresponding increase in another variable
and vice versa, then the variables are considered
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to be positively correlated.
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For example: profit and investment.
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On the contrary, when the two variables move
in different directions, in such a way that,
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an increase in one variable, will result in
a decrease in another variable and vice versa,
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this situation is known as negative correlation.
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For example: Price and demand of a product.
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Correlation Analysis
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The degree of association, is measured by
a correlation coefficient, denoted by r.
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It is sometimes called, Pearson's correlation
coefficient, after its originator and is a
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measure of linear association.
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If a curved line is needed to express the
relationship, other and more complicated measures
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of the correlation, must be used.
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The correlation coefficient is measured on
a scale, that varies from + 1 through 0 to
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- 1.
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Complete correlation between two variables
is expressed by either + 1 or -1.
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When one variable increases as the other increases
the correlation is positive; when one decreases
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as the other increases it is negative.
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Complete absence of correlation is represented
by 0.
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This figure gives some graphical representations
of correlation.
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Calculating Correlation Coefficient
This coefficient is easily calculated by using
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Microsoft Excel and Minitab very easily.
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Correlation Coefficient by Excel
There are 02 methods to calculate the correlation
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coefficient in Excel.
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Method-01):
Let’s take an earlier example of Temperature
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of the day vs Ice cream sales.
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To determine the correlation between these
02 variables, use the function CORREL.
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Type the function CORREL and select 1st variable
column values and apply comma.
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After that, select 2nd variable column and
press Enter.
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We will get the value of correlation coefficient
as 0.96
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It means, there is a strong relationship between
the variables.
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Method-02):
Let’s continue with the same example.
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To determine relationship between these 02
variables, use the Analysis Toolpak add-in
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in Excel to quickly generate correlation coefficients
between multiple variables, and execute the
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following steps.
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1.
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On the Data tab, in the Analysis group, click
Data Analysis.
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2.
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Select Correlation and click OK.
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3.
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Select the range A1:B13 as the Input Range,
Check Labels in the 1st row and select output
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range anywhere in the sheet or new worksheet
option and click OK.
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4.
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We will get the final results as below:
It is showing same value of correlation coefficient
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i.e. 0.96 indicates strong relationship between
variables.
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Regression
We have seen that, correlation describes the
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strength of an association between two variables,
and is completely symmetrical, the correlation
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between A and B is the same as the correlation
between B and A.
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However, if the two variables are related
it means that when one changes by a certain
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amount the other changes on an average by
a certain amount.
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If y represents the dependent variable and
x the independent variable, this relationship
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is described as the regression of y on x.
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The relationship can be represented by a simple
equation called the regression equation.
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In this context "regression" simply means
that the average value of y is a "function"
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of x, that is, it changes with x.
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The regression equation representing how much
y changes with any given change of x, can
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be used to construct a regression line on
a scatter diagram, and in the simplest case
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this is assumed to be a straight line.
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I am not going in further details as we can
easily found it by using simple software like
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Microsoft excel.
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Let’s continue with the same example of
Temperature of the day and ice cream sale
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to understand regression analysis in Excel
and how to interpret the Summary Output.
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1.
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On the Data tab, in the Analysis group, click
Data Analysis.
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2.
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Select Regression and click OK.
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3.
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Select the Y Range (B1:B13).
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This is the predictor variable (also called
the dependent variable).
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4.
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Select the X Range (A1:A13).
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These are the explanatory variables (also
called independent variables).
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These columns must be adjacent to each other.
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5.
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Check Labels.
6.
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Click in the Output Range box and select cell
A16.
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(You can select anywhere in the sheet as well
as in a separate worksheet)
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7.
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Check Residuals.
8.
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Click OK.
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Excel produces the following Summary Output
(rounded it to 3 decimal places).
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R Square
R Square equals 0.917, which is a very good
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fit.
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92% of the variation in Ice cream sales is
explained by the Temperature of the day.
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The closer to 1, the better the regression
line fits the data.
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Significance F and P-values
To check if your results are reliable (statistically
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significant), look at Significance F (0.000).
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If this value is less than 0.05, you're OK.
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If Significance F is greater than 0.05, it's
probably better to stop using this set of
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independent variables.
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Delete a variable with a high P-value (greater
than 0.05) and rerun the regression until
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Significance F drops below 0.05.
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Most or all P-values should be below 0.05.
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In our example, this is the case.
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(0.015 and 0.000).
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Coefficients
The regression line is: y = Ice cream sale
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= -159.474+ 30.088 * Temperature of the day.
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In other words, for each unit increase in
Temperature, Ice cream sale increases by 30.088
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units.
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This is valuable information.
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You can also use these coefficients to do
a forecast.
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Residuals
The residuals show you how far away the actual
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data points are from the predicted data points
(using the equation).
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For example, the first data point equals 215.
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Using the equation, the predicted data point
equals
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-159.474+ 30.088 * 14.2= 267.773, giving a
residual of 267.773 - 215 = -52.773
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Conclusion:
With the above discussion, it is evident,
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that there is a big difference between these
two mathematical concepts, although these
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two are studied together.
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Correlation is used when the researcher wants
to know whether the variables under study
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are correlated or not, if yes then what is
the strength of their association?
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In regression analysis, a functional relationship
between two variables is established so as
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to make future projections
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on events.
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