This model type is one of the building blocks of machine learning. This is done with the following code block. In our case, we will keep increasing the degree of the input features until the MSE does not increase by 0.02 then we will stop training. We will also set a threshold for which the MSE must increase for us to continue to increase complexity. We can use this dataset to test the model performance on “unseen data”. A simple way to solve this problem is using a validation dataset. We need to choose a model that picks up on the general patterns of the data, but not the random patterns of the training data. If we get a new sample of data points, we want to make sure that the model fits well to those points as well. If we keep adding more and more columns to the X matrix, then we will fit the data better and better.Ĭareful! The more we increase the complexity of the line, the higher the risk of overfitting the training data. This model fits much better! Simply adding the squared values of the data points improved the simple linear regression model. The equation for this line is shown below. Simply, it is choosing the line of best fit. It chooses these parameters by minimizing the sum of the squares of the differences between the observed labels and the predicted labels.

Ordinary least squares is the method used to find the unknown parameters of a linear regression model. In the following section, we can find the equation of this line using ordinary least squares. We could simply draw a line that looks good to the eye, but to make a really good guess, we will need to work on some mathematics. This way given any temperature measurement, we are able to provide an accurate estimate of its salinity. There are many ways of tackling this problem, but one of the most common ways is to draw a line that fits the data. Could we estimate its salinity value based on temperature? (Surprise! Yes we can.) Now let’s say we were given a new data point that had a temperature measurement, but no salinity value.

Simple linear regression equation b0