Linear Regression: Revision

You practised linear regression modelling in the previous sessions. Let’s revise some of the concepts you learnt.

Here, Ujjyaini mentioned that regression guarantees interpolation of data and not extrapolation.

Interpolation means using the model to predict the value of a dependent variable on the independent values that lie within the range of data you already have. Extrapolation, on the other hand, means predicting the dependent variable on the independent values that lie outside the range of the data the model was built on.

To understand this better, look at the diagram below. The model is built on the values of x between a and b.

When you wish to predict the Y for X1, which lies between a and b, it is called interpolation. On the other hand, extrapolation would be extending the line to predict Y for X2, which lies outside the range on which the linear model was trained.

For now, you only need to understand what these terms mean. You will learn more about these in the upcoming lectures.

Ujjyaini also mentioned that linear regression is a parametric model.

Even though a detailed discussion on parametric and non-parametric models is beyond the scope of this module, a simple explanation is given below. You may also refer to the additional resources provided below.

In simple terms, a parametric model can be described using a finite number of parameters. For e.g., a linear regression model built using n independent variables will have exactly n ‘parameters’ (i.e., n coefficients). The entire model can be described using these n parameters.

In the upcoming modules, you will learn about some non-parametric models as well, such as decision trees.

They do not have a finite set of parameters that completely describe the model.

To read more on this topic further, here are some useful links:

• Parametric vs non-parametric models in brief
• A detailed explanation of parametric and non-parametric models

It is very crucial to understand when to apply linear regression modelling. Let's go through some business cases to understand where you can apply linear regression modelling.

You saw various cases and learnt where linear regression modelling can be used and where it cannot. Answer the question below to test your understanding.