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# Linear and Non-Linear Trendlines in Python

Add linear Ordinary Least Squares (OLS) regression trendlines or non-linear Locally Weighted Scatterplot Smoothing (LOEWSS) trendlines to scatterplots in Python.

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New to Plotly?

Plotly is a free and open-source graphing library for Python. We recommend you read our Getting Started guide for the latest installation or upgrade instructions, then move on to our Plotly Fundamentals tutorials or dive straight in to some Basic Charts tutorials.

### Linear fit trendlines with Plotly Express¶

Plotly Express is the easy-to-use, high-level interface to Plotly, which operates on a variety of types of data and produces easy-to-style figures.

Plotly Express allows you to add Ordinary Least Squares regression trendline to scatterplots with the trendline argument. In order to do so, you will need to install statsmodels and its dependencies. Hovering over the trendline will show the equation of the line and its R-squared value.

In [1]:
import plotly.express as px

df = px.data.tips()
fig = px.scatter(df, x="total_bill", y="tip", trendline="ols")
fig.show()


### Fitting multiple lines and retrieving the model parameters¶

Plotly Express will fit a trendline per trace, and allows you to access the underlying model parameters for all the models.

In [2]:
import plotly.express as px

df = px.data.tips()
fig = px.scatter(df, x="total_bill", y="tip", facet_col="smoker", color="sex", trendline="ols")
fig.show()

results = px.get_trendline_results(fig)
print(results)

results.query("sex == 'Male' and smoker == 'Yes'").px_fit_results.iloc[0].summary()

      sex smoker                                     px_fit_results
0  Female     No  <statsmodels.regression.linear_model.Regressio...
1  Female    Yes  <statsmodels.regression.linear_model.Regressio...
2    Male     No  <statsmodels.regression.linear_model.Regressio...
3    Male    Yes  <statsmodels.regression.linear_model.Regressio...

Out[2]:
Dep. Variable: R-squared: y 0.232 OLS 0.219 Least Squares 17.56 Mon, 23 Nov 2020 9.61e-05 18:29:35 -101.03 60 206.1 58 210.2 1 nonrobust
coef std err t P>|t| [0.025 0.975] 1.4253 0.424 3.361 0.001 0.576 2.274 0.0730 0.017 4.190 0.000 0.038 0.108
 Omnibus: Durbin-Watson: 21.841 1.383 0 33.031 1.315 6.72e-08 5.51 60.4

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

### Non-Linear Trendlines¶

Plotly Express also supports non-linear LOWESS trendlines.

In [3]:
import plotly.express as px

df = px.data.gapminder().query("year == 2007")
fig = px.scatter(df, x="gdpPercap", y="lifeExp", color="continent", trendline="lowess")
fig.show()


Dash is an open-source framework for building analytical applications, with no Javascript required, and it is tightly integrated with the Plotly graphing library.

Learn about how to install Dash at https://dash.plot.ly/installation.

Everywhere in this page that you see fig.show(), you can display the same figure in a Dash application by passing it to the figure argument of the Graph component from the built-in dash_core_components package like this:

import plotly.graph_objects as go # or plotly.express as px
fig = go.Figure() # or any Plotly Express function e.g. px.bar(...)