Scatter Plot Regression Line

Scatter plot

Scatter plots show the relationship among two variables by displaying data points on a two-dimensional graph. The variable that might be measured an explanatory variable is plotted on the x axis, and the reply variable is plotted on the y axis.

Regression line:

From a given scatter plots we can draw the best fit line that is known as regression line. The regression line is can be calculated by using least squares method because the regression line drawn by eyes will causes wide variations and it is not accurate one.


Least Squares method to get regression line

This method is based on the sum of the squares of the deviations of all coordinates from the regression line is at a minimum. In a graph, variable y is dependent one because the values of y are calculated from the independent variable x. The most suitable regression line contains the best fit of y on x.  The regression of x on y gives a different regression line which is not a correct one. The best fit line is described by

yn = c + dx

Here yn is the dependent variable and dx is the independent variable. The values of yn  is calculated based on the value of dx, c is the y intercept .

The value of c is calculated by

c = yn- dx

The value of d is the slope of the best fit line and it is calculated by

d =`"(n(Sigmaxy)- (Sigmax)(Sigmay))/(n(Sigmax)-(Sigmax)^2) `

Here n is the number of pair of the data.

Types of slope of regression line:

Types of slope of regression line:

Regression line through positive slope

Regression line through negative slope

Regression line through zero slopes.

Condition for positive slope:

The rate of y increases as the rate of x increases.


Condition for negative slope:

The rate of y decreases as the rate of x increases.



Condition for zero slopes:

No relation along with the variables x and y.