# Essay on Linear Regression Is Measured By Using Lines Of Regression

By p Nitin

Feb 16, 2013

Linear Regression Definition states that it can be measured by using lines of regression. Regression measures the amount of average relationship or mathematical relationship between two variables in terms of original units of data. Whereas, correlation measures the nature of relationship between two variables. i.e.., positive or negative or uncorrelated.

Regression is used for estimating the value of one variable if you know the value of other variable. i.e.., One of the variable is independent variable and other variable is dependent variable.

Let ( Xi , Yi ) ; i = 1, 2, 3, ...................n the n pairs of observations are given now plot all these points in XY-plane which reserves a scatter diagram. In scatter diagram if the maximum number of points are going through a straight lines then we call it as linear regression if not that means they are passing through a curve then we call it as curve linear regression. Linear Regression can be measured by using lines of regreesion i.e.., Y-on-X & X-on-Y and also curve linear regression can be measured by using correlation ratio.

Linear Regression Equation

The linear regression formula is derived as follows. Let ( Xi , Yi ) ; i = 1,2,3,................ n be n-pairs of observations are given and there are representing a linear regression.

We know that, coefficient of correlation

r = cov ( X , Y ) / (sigmaX sigmaY ) where cov ( X , Y ) = ( 1/n) sum XiYi - barX barY

and X2 = (1/n)…