In statistics,Linear regression is the linear approximation of the causal relationship between the two variables. This model has one independent variable and one dependent variable.The model which has one dependent variable is called Simple Linear Regression.

Uses of this model

Linear regression is used to predict,forecast and error reduction.

This model also can be used to establish quantified relationship between explanatory variables and response.

Interpretation

This model can be interpreted as ,

Y’ = bX + A

Here Y’ is the predicted value(dependent variable)

X is the independent variable

b is constant

A is error of estimation

Note: The (y-y’)**2 value of the regression line is the least in the linear regression model. In other words the regression line is the line which has most observations nearer.

Example

Let us try to understand this model through an example:

There is a popular ice cream store who had an executive meeting where sudden surge in sale came to their attention and they tried to understand the reasons.They figured out that the increase in temperature caused their increase in sales.They are trying to use this information to predict their business.The Linear Regression model came in to the picture now as they tried to quantify the relationship between the variables.

Here the relationship between the temperature and sales can be defined using this regression model which in turn helped them to predict their sales.

If the graph is plotted using these variables for a sample information it would be as follows:

Note:Always consider units of measurement of variables when constructing a model.

From the above graph it is established a quantified relationship between temperature and sales and can predict that their sales can be approximated depending on the temperature.

Conclusion

In spite of errors in prediction, the Simple Linear regression is the basic and most useful model in Machine learning for its effectiveness in establishing a quantified relationship between the variables which helps in prediction and forecasting.

Nicely written, Good Example!