How To Run Linear Regressions In Python Scikit-learn
Before we start: This Python tutorial is a part of our series of Python Package tutorials.
Scikit-learn is a Python package that simplifies the implementation of a wide range of Machine Learning (ML) methods for predictive data analysis, including linear regression.
Linear regression can be thought of as finding the straight line that best fits a set of scattered data points:
You can then project that line to predict new data points. Linear regression is a fundamental ML algorithm due to its comparatively simple and core properties.
Linear Regression Concepts
A basic understanding of statistical math is key to comprehending linear regression, as is a good grounding in ML concepts.
For more information on ML concepts and terminology, refer to: What is Scikit-Learn In Python?
The following are some key concepts you will come across when you work with scikit-learn’s linear regression method:
- Best Fit – the straight line in a plot that minimizes the deviation between related scattered data points.
- Coefficient – also known as a parameter, is the factor a variable is multiplied by. In linear regression, a coefficient represents changes in a Response Variable (see below).
- Coefficient of Determination – the correlation coefficient denoted as 𝑅². Used to describe the precision or degree of fit in a regression.
- Correlation – the relationship between two variables in terms of quantifiable strength and degree, often referred to as the ‘degree of correlation’. Values range between -1.0 and 1.0.
- Dependent Feature – a variable denoted as y in the slope equation y=ax+b. Also known as an Output, or a Response.
- Estimated Regression Line – the straight line that best fits a set of scattered data points.
- Independent Feature – a variable denoted as x in the slope equation y=ax+b. Also known as an Input, or a predictor.
- Intercept – the location where the Slope intercepts the Y-axis denoted b in the slope equation y=ax+b.
- Least Squares – a method of estimating a Best Fit to data, by minimizing the sum of the squares of the differences between observed and estimated values.
- Mean – an average of a set of numbers, but in linear regression, Mean is modeled by a linear function.
- Ordinary Least Squares Regression (OLS) – more commonly known as Linear Regression.
- Residual – vertical distance between a data point and the line of regression (see Residual in Figure 1 below).
- Regression – estimate of predictive change in a variable in relation to changes in other variables (see Predicted Response in Figure 1 below).
- Regression Model – the ideal formula for approximating a regression.
- Response Variables – includes both the Predicted Response (the value predicted by the regression) and the Actual Response, which is the actual value of the data point (see Figure 1 below).
- Slope – the steepness of a line of regression. Slope and Intercept can be used to define the linear relationship between two variables: y=ax+b.
- Simple Linear Regression – a linear regression that has a single independent variable.
Figure 1. Illustration of some of the concepts and terminology defined in the above section, and used in linear regression:
Linear Regression Class Definition
A scikit-learn linear regression script begins by importing the LinearRegression class:
from sklearn.linear_model import LinearRegression sklearn.linear_model.LinearRegression()
Although the class is not visible in the script, it contains default parameters that do the heavy lifting for simple least squares linear regression:
sklearn.linear_model.LinearRegression(fit_intercept=True, normalize=False, copy_X=True)
Calculate the intercept for the model. If set to False, no intercept will be used in the calculation.
Converts an input value to a boolean.
Copies the X value. If True, X will be copied; else it may be overwritten.
How to Create a Linear Regression Model
In this example, a linear regression model is created based on data in a numpy array. The coefficients are formulated and then printed in the console:
# Import the packages and classes needed in this example: import numpy as np from sklearn.linear_model import LinearRegression # Create a numpy array of data: x = np.array([6, 16, 26, 36, 46, 56]).reshape((-1, 1)) y = np.array([4, 23, 10, 12, 22, 35]) # Create an instance of a linear regression model and fit it to the data with the fit() function: model = LinearRegression().fit(x, y) # The following section will get results by interpreting the created instance: # Obtain the coefficient of determination by calling the model with the score() function, then print the coefficient: r_sq = model.score(x, y) print('coefficient of determination:', r_sq) # Print the Intercept: print('intercept:', model.intercept_) # Print the Slope: print('slope:', model.coef_) # Predict a Response and print it: y_pred = model.predict(x) print('Predicted response:', y_pred, sep='\n')
Watch how to create a Linear Regression and then print the Coefficients
How to Create a Linear Regression and Display it
In this example, random data is displayed in a plot. A linear regression model is then created against the data, and an estimated regression line is finally displayed.
# Import the packages and classes needed for this example: import numpy as np import matplotlib.pyplot as plt from sklearn.linear_model import LinearRegression # Create random data with numpy, and plot it with matplotlib: rnstate = np.random.RandomState(1) x = 10 * rnstate.rand(50) y = 2 * x - 5 + rnstate.randn(50) plt.scatter(x, y); plt.show() # Create a linear regression model based the positioning of the data and Intercept, and predict a Best Fit: model = LinearRegression(fit_intercept=True) model.fit(x[:, np.newaxis], y) xfit = np.linspace(0, 10, 1000) yfit = model.predict(xfit[:, np.newaxis]) # Plot the estimated linear regression line with matplotlib: plt.scatter(x, y) plt.plot(xfit, yfit); plt.show()
Watch how to create a Linear Regression and display it in a Plot
Regression vs Classification
The main difference between regression and classification is that the output variable in regression is continuous, while the output for classification is discrete. Regression predicts quantity; classification predicts labels.
For information about classification, refer to: How to Classify Data in Python
The following tutorials will provide you with step-by-step instructions on how to work with machine learning Python packages:
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