11.4 : Regression Analysis

Regression analysis is a statistical method of developing a mathematical model to estimate a relationship between the variables. It is used to predict the value of a dependent variable based on another independent variable.

For example, consider a data set having a strong linear relationship with a correlation coefficient of 0.892. 

A best-fit line passing through the scatter plot is the regression line.

The algebraic equation of the regression line is known as the regression equation.

It expresses the relationship between the carbon dioxide levels, x, the independent variable, and the annual temperature, y, the dependent variable.

Here, b₀ is the y-intercept, and b₁ is the slope of the regression line.

As the regression line shows a good fit, the regression equation can be used to predict the annual temperature for, say, a carbon dioxide level of 380 ppm.

This value is put in the regression equation to obtain the predicted annual temperature of 14.7 degrees Celsius.