simple linear regression equation statistics

Note: We’ll use the OLS() function from the statsmodels library to fit the regression model. Once we’ve confirmed that the relationship between our variables is linear and that there are no outliers present, we can proceed to fit a simple linear regression model using hours as the explanatory variable and score as the response variable: There are no tiny circles in the boxplot, which means there are no outliers in our dataset. If an observation is an outlier, a tiny circle will appear in the boxplot: df. By default, Python defines an observation to be an outlier if it is 1.5 times the interquartile range greater than the third quartile (Q3) or 1.5 times the interquartile range less than the first quartile (Q1). Next, we can create a boxplot to visualize the distribution of exam scores and check for outliers. As hours increases, score tends to increase as well in a linear fashion. Exam Score')įrom the plot we can see that the relationship does appear to be linear. We can create a simple scatterplot to view the relationship between the two variables: import matplotlib.pyplot as plt DataFrame()īefore we fit a simple linear regression model, we should first visualize the data to gain an understanding of it.įirst, we want to make sure that the relationship between hours and score is roughly linear, since that is an underlying assumption of simple linear regression. The following code shows how to create this fake dataset in Python: import pandas as pdĭf = pd. We’ll attempt to fit a simple linear regression model using hours as the explanatory variable and exam score as the response variable. Step 1: Load the Dataįor this example, we’ll create a fake dataset that contains the following two variables for 15 students: This tutorial provides a step-by-step explanation of how to perform simple linear regression in Python.

This equation can help us understand the relationship between the explanatory and response variable, and (assuming it’s statistically significant) it can be used to predict the value of a response variable given the value of the explanatory variable.

b 0: The intercept of the regression line.

This technique finds a line that best “fits” the data and takes on the following form: Simple linear regression is a technique that we can use to understand the relationship between a single explanatory variable and a single response variable.

Simple linear regression equation statistics