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Regression Analysis
Regression analysis is a method of measuring the degree of association of a set of variables called cause variables over the effect variable. It can give the answer to questions like if pollution causes the bad impact on health what level of impact on health can be expected from 10 point increase in pollution level? Correlation can only measure the direction of the increase in pollution level that is positive negative or zero association whereas regression can measure both directions as well as the degree of association. If we have two variables, X and Y then the correlation between X and Y is equal to Y and X. So both variables can be interchanged in correlation however in regression, variables are not interchangeable as one variable is a cause and the other variable is the effect. For example, population growth depends on time but time does not depend on population growth, Maize productions may depend on rainfall but rainfall doesn’t depend on production. Thus in regression, we must define which one is a cause and which one is effect variable. Cause and effect variables are also termed as independent and dependent variables.
Regression is one of the highest used data analysis by researchers and academicians today. The method of regression was introduced by Francis Galton.
Types of regression:
Difference between Correlation and Regression:
The following are the differences between the correlation and regression.
Lines of regression
Whenever a line shows a relationship between the two variables, the dots of the scatter diagram will concentrate around a certain curve. If the curve is a straight line, then it is known as the line of regression.
A line of regression gives the best the best estimate ( in the sense of least square method) of one variable for a given value of the other variable. So, there are in general two lines of regression. One is the line of regression of y on x giving the best-estimated value of y whenever the value of x is known. Other is the line of regression of x on y giving the best-estimated value of x whenever the value of y is known. The two lines of regression intersect at the point ( \(\overline{x},\;\overline{y})\;)\;\overline{x}\;and\;\overline{y}\) being the averages of x and y. If there is a wide gap between the two lines of regression intersect at right angles, there is no correlation between the two variables.
Let us see the following graphs of lines of regression presenting the correlation between two variables:
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Taken reference from
( Basic mathematics Grade XII and A foundation of Mathematics Volume II and Wikipedia.com )
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