Simple Linear Regression
Simple Linear Regression
Simple linear regression is a regression model that estimates the relationship between one independent variable and one dependent variable using a straight line. Both variables should be in quantitative variables.
Example 1) How strong the relationship are between two variables are (e.g The relation between Study and marks).
Example 2) The value of the dependent variable at a certain value of the independent variable. (eg. The more efforts you take the more marks you will score ,The less efforts you take the less marks you will score).
How to perform simple linear regression :-
The formula for simple linear regression is :-
Y=B0 + B1X
· Here Y is the predicted value of dependent variable (y) for the given value of independent variable (x)
· B0 is intercept as predicted value of y when the x is 0.
· B1 is regression coefficient — here we expect y to change as the x increases.
· X is the independent variable.
Simple linear regression line can show a positive linear relationships, negative linear relationship and no relationship.
1) No relationship :- The graph line in the simple linear regression is flat and it is not sloped. And there is no relation between two variables.
2) Positive relationship :- In this relation the regression line are slope upward with lower end of the line at Y intercept of graph and the upper end of line extend upward in the graph field far from the x axis. In positive relationship it is a positive linear relation between two variables: as one value increases the value of other also increases.
3) Negative relationship :- In this relationship the regression line slope are in downward with the upper end of line and the y axis of graph at the lower end of line increasing downward in the graph field towards the x axis. In this relationship it is negative linear relationship between the two variables as one of the value increases, the value of other decreases.
Assumptions of simple linear regression :-
Simple linear regression takes certain assumptions about the data. The Assumptions are :-
1) Homogeneity of variance (Homoscedasticity):-
In this assumption the size of error in the prediction does not change significantly across the values of the independent variable.
2) Independence of observations :-
In this assumption the observation of the dataset are collected by statistical and sampling method and there are no hidden relationship among the observations.
3) Normality:-
In this observation the data follows the normal distribution.
Methods of simple linear regressions:-
Simple linear regression is a statistical method that allow us to study the relationship between two quantitative variables :-
One variable, denoted X is considered as predictor variable, explanatory variable or independent variable.
