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TOPIC 6 : REGRESSION & CORRELATION, image and image Hence, image…
TOPIC 6 : REGRESSION & CORRELATION
Scatter Plot
It serves as a helpful summary of a set of bivariate data (two variables), and is typically created before calculating a linear correlation coefficient or fitting a regression line.
It helps with the interpretation of the correlation coefficient or regression model by providing a clear visual representation of the relationship between the two variables.
A plot of the paired observations is known as a scatter plot or scatter diagram.
The plot's pattern reveals the nature and significance of the relationship between the two variables.
Steps to Slove Simple Linear Regression Problem
Construct the following table to facilitate computation
Calculate the linear regression parameters
using the formula as
Draw the scatter plot of the (X,Y) data for visual inspection of the relationship
that may exist between X and Y.
The linear regression model of the data is given by
by substitute the values of
and
Correlation
Population correlation coefficient
defined as
Estimated Regression Model
Each line has different values such as the slope
and the y-intercept
The scatter plot can be many straight lines (regression models).
Use the least squares method to locate the line that fits the scatter plot's points the best.
to determine a least square regression line, which is the best fit line.
The estimaded least square regression lin may written as
and
Hence,
where
= mean of y =
,
=mean of x =
and n = sampe size
