Subject: Mathematics

**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:**

- If we only have one cause for an effect then it is called simple regression.
- If the causes are more that one, for an effect then it is called a multiple regression. For example, Growth of bacteria in a food may depend on the nature of food but also depends on temperature, moisture content, time storage etc. Thus if a researcher assumes that the growth of bacteria is primarily due to the temperature of store room then he will use a simple regression with the assumption that the effect of other causes is not very significant.
- If the same unit change in cause variable makes a change of constant magnitude in effect variable it is called linear regression. A linear regression is expressed by the equation of a line.
- If the unit change in a cause does not make a constant change in effect it is called non-linear regression, which cannot be expressed by a line but by higher order polynomials.

**Difference between Correlation and Regression:**

The following are the differences between the correlation and regression.

- Correlation means the relationship between the two variables such that the change in the value of one variable results changes in the value of the other variable. But regression means returning back to the average value.
- There is no need of cause and effect relationship between the two variables in case of correlation but there must be cause and effect relationship between two variables in case of regression.
- Correlation analysis presents the extent to which the two variables are correlated and also the direction of their movements. But regression analysis aims to study the nature of the relationship between the two variables so that we may be able to find the value of one variable when the value of the other variable is known.
- The correlation coefficient is independent of the change of origin and scale but regression coefficients are independent of the change of origin but not of scale.
- The correlation coefficient between the two variables can not exceed 1 but the regression coefficient can exceed 1 and other regression coefficients less than 1 making their product less than or equal to 1.

**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 )

- Regression analysis is a method of measuring the degree of association of a set of variables called cause variables over the effect variable.
- Correlation means the relationship between the two variables such that the change in the value of one variable results changes in the value of the other variable. But regression means returning back to the average value.

- It includes every relationship which established among the people.
- There can be more than one community in a society. Community smaller than society.
- It is a network of social relationships which cannot see or touched.
- common interests and common objectives are not necessary for society.

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