Hello everyone, welcome to the course of machine learning with Python. In this video, we should see how to solve linear regression problem by normal equation and also how to solve this using the inbuilt function in the Python library cycler. So we have already seen these data set in our last Python video, so we'll be using the same data set. Now, the first tip would be to update a column of all ones to the left of the training data set. So that what we have done over here, so we have appended a column of all one values to the length of the training data set, and we have created a new data set which is x underscore t, then using the normal equation, we have obtained the value of the model parameters. Note that here we have used NP dot linear algebra or lie in G dot p in to compute the inverse of X underscore P transpose and x t multiplied with x t. So, why do we have use p in so this is stands for pseudo inverse.

So as we have already described when ever there is the X transpose X is singular or is not invertible we'll be using pseudo inverse, okay, but here it is always recommended to use pseudo inverse because whether the matrix X transpose X is singular or not pseudo inverse will always work. Okay, so let's go ahead and run this particular cell and we'll be printing the value of the data that we have obtained using the normal equation. Now, the values of the data that we have obtained using gradient descent is this one. Note that the values are quite similar. Now the predicted values of y in the test data set we can opt in like these, and this is the actual values versus the predicted values for normal equation and the mean squared error cost would be Is 7.469 Now we should solve for the linear regression by inbuilt function in the Python library called scikit learn or the scalar.

So for that from SK learn dot linear model, we'll import a class called linear regression. Now this model is nothing but an instance of the object of this particular class linear regression, which is fitted on the training data extract and wireframe, let's go ahead and run this particular cell. Now inside the attribute called co e f underscore the coefficient of the models are stored. So these are basically the coefficients and the intercept is so interested is nothing but a zero value and the coefficients are nothing but all other values other than theta zero. So as you can see, there are also very much similarity between the results obtained in the gradient descent and the normal equation to that in the value update in the inbuilt Python Pretty all the inbuilt function in the Python library cycler Okay, so similarly we'll go ahead and predict the value of y for the test dataset okay.

Note that here we need not to do any kind of appending of all ones because inside this function or inside this linear regression model everything will be taken care of okay. So you need not to obtain any polyp of all ones when you use the inbuilt scikit learn library functions okay. They can we compare the predictive value with the actual value and the mean squared error cost will be this one okay. So, that is how we can obtain a very good linear regression model using the inbuilt function inside the Python library called scikit learn so I will recommend to use that. So, in this particular video, we have seen how to leverage the idea of normal equation and also we have seen how to use the inbuilt function Inside the Python library called scikit learn in order to solve the linear regression problem. Okay, so in the next video, we shall see how to use polynomial regression in Python.

See you in the next lecture. Thank you.