Meaning of simple linear regression
- It offers the relationship between two variables, namely the dependent and the independent variable.
- It is also known as 'ordinary least squares' or OLS regression.
- It is a tool used in forecasting and financial analysis.
Important terms
*Independent and Dependent variable *This is best understood with an example. Say, you wish to forecast the changes in the profits of the company due to an increase in the overall volume of sales of the company. Then the profits are the dependent variables and they depend on the quantum of increase in the sales, and the volume of sales would be the independent variable.
*Covariance *The formula that establishes a relationship between two variables is covariance. Cov(x,y)=∑(xn−xu)(yn−yu)/N The number calculated cannot be used for direct interpretation as it is not standardised. This can be done with the help of correlation coefficient.
*Correlation coefficient *It is the covariance divided by the product of standard deviation of the two variables x and y binding the correlation between the values of positive one and negative one. Correlation=ρxy = Covxy / sxsy For instance, if the correlation turns out to be +1, then it can be reasonably concluded that a 1% increase in the sales volume would result in 1% increase in the profit of the company. The converse would operate if the value is -1.
Regression Equation
It is calculated as follows –
Y = bx + a + e
Where,
Y= value that we are trying to forecast
b = slope of the regression line
x = value of our independent value
a = y-intercept (it is a constant)
e = residual error
Fundamental Assumptions of the Linear Model
- Independent variables are not random.
- Value of the residual or the error is zero.
- Value of the residual or the error is constant across all observations.
- Value of the residual or the error is not correlated across all observations.
- The residual or the error values follow the normal distribution.
- Dependent and independent variables show a linear relationship between the slope and the intercept.
