Machine Learning - Linear Regression

The term regression is used when you try to find the relationship between variables. In Machine Learning, and in statistical modeling, that relationship is used to predict the outcome of future events.

This line can be used to predict future values. In Machine Learning, predicting the future is very important.

We will show you how to use these methods instead of going through the mathematic formula. In the example below, the x-axis represents age, and the y-axis represents speed. We have registered the age and speed of 13 cars as they were passing a tollbooth. Let us see if the data we collected could be used in a linear regression:

Start by drawing a scatter plot: import matplotlib.pyplot as plt x = [5,7,8,7,2,17,2,9,4,11,12,9,6] y = [99,86,87,88,111,86,103,87,94,78,77,85,86] plt.scatter(x, y) plt.show()

Import scipy and draw the line of Linear Regression: import matplotlib.pyplot as plt from scipy import stats x = [5,7,8,7,2,17,2,9,4,11,12,9,6] y = [99,86,87,88,111,86,103,87,94,78,77,85,86]

Import the modules you need. You can learn about the Matplotlib module in our Matplotlib Tutorial. You can learn about the SciPy module in our SciPy Tutorial. import matplotlib.pyplot as plt from scipy import stats Create the arrays that represent the values of the x and y axis: x = [5,7,8,7,2,17,2,9,4,11,12,9,6] y = [99,86,87,88,111,86,103,87,94,78,77,85,86] Execute a method that returns some important key values of Linear Regression:

Create a function that uses the slope and intercept values to return a new value. This new value represents where on the y-axis the corresponding x value will be placed:

plt.scatter(x, y) Draw the line of linear regression: plt.plot(x, mymodel)

plt.show()

It is important to know how the relationship between the values of the x-axis and the values of the y-axis is, if there are no relationship the linear regression can not be used to predict anything.

means 100% related. Python and the Scipy module will compute this value for you, all you have to do is feed it with the x and y values.

How well does my data fit in a linear regression? from scipy import stats x = [5,7,8,7,2,17,2,9,4,11,12,9,6] y = [99,86,87,88,111,86,103,87,94,78,77,85,86]

The result -0.76 shows that there is a relationship, not perfect, but it indicates that we could use linear regression in future predictions.

Now we can use the information we have gathered to predict future values.

Example: Let us try to predict the speed of a 10 years old car. To do so, we need the same myfunc() function from the example above:

Predict the speed of a 10 years old car: from scipy import stats x = [5,7,8,7,2,17,2,9,4,11,12,9,6] y = [99,86,87,88,111,86,103,87,94,78,77,85,86]

The example predicted a speed at 85.6, which we also could read from the diagram:

Let us create an example where linear regression would not be the best method to predict future values.

import matplotlib.pyplot as plt from scipy import stats x = [89,43,36,36,95,10,66,34,38,20,26,29,48,64,6,5,36,66,72,40] y = [21,46,3,35,67,95,53,72,58,10,26,34,90,33,38,20,56,2,47,15]

for relationship?

value. import numpy from scipy import stats x = [89,43,36,36,95,10,66,34,38,20,26,29,48,64,6,5,36,66,72,40] y = [21,46,3,35,67,95,53,72,58,10,26,34,90,33,38,20,56,2,47,15]

The result: 0.013 indicates a very bad relationship, and tells us that this data set is not suitable for linear regression.