Linear and Non-Linear Trendlines in Python

Add linear Ordinary Least Squares (OLS) regression trendlines or non-linear Locally Weighted Scatterplot Smoothing (LOWESS) trendlines to scatterplots in Python. Options for moving averages (rolling means) as well as exponentially-weighted and expanding functions.

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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]:

OLS Regression Results
Dep. Variable:	y	R-squared:	0.232
Model:	OLS	Adj. R-squared:	0.219
Method:	Least Squares	F-statistic:	17.56
Date:	Fri, 15 Sep 2023	Prob (F-statistic):	9.61e-05
Time:	16:57:24	Log-Likelihood:	-101.03
No. Observations:	60	AIC:	206.1
Df Residuals:	58	BIC:	210.2
Df Model:	1
Covariance Type:	nonrobust

	coef	std err	t	P>\|t\|	[0.025	0.975]
const	1.4253	0.424	3.361	0.001	0.576	2.274
x1	0.0730	0.017	4.190	0.000	0.038	0.108

Omnibus:	21.841	Durbin-Watson:	1.383
Prob(Omnibus):	0.000	Jarque-Bera (JB):	33.031
Skew:	1.315	Prob(JB):	6.72e-08
Kurtosis:	5.510	Cond. No.	60.4

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

Displaying a single trendline with multiple traces¶

new in v5.2

To display a single trendline using the entire dataset, set the trendline_scope argument to "overall". The same trendline will be overlaid on all facets and animation frames. The trendline color can be overridden with trendline_color_override.

In [3]:

import plotly.express as px

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

In [4]:

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", trendline_scope="overall", trendline_color_override="black")
fig.show()

OLS Parameters¶

new in v5.2

OLS trendlines can be fit with log transformations to both X or Y data using the trendline_options argument, independently of whether or not the plot has logarithmic axes.

In [5]:

import plotly.express as px

df = px.data.gapminder(year=2007)
fig = px.scatter(df, x="gdpPercap", y="lifeExp", 
                 trendline="ols", trendline_options=dict(log_x=True),
                 title="Log-transformed fit on linear axes")
fig.show()

In [6]:

import plotly.express as px

df = px.data.gapminder(year=2007)
fig = px.scatter(df, x="gdpPercap", y="lifeExp", log_x=True, 
                 trendline="ols", trendline_options=dict(log_x=True),
                 title="Log-scaled X axis and log-transformed fit")
fig.show()

Locally WEighted Scatterplot Smoothing (LOWESS)¶

Plotly Express also supports non-linear LOWESS trendlines. In order use this feature, you will need to install statsmodels and its dependencies.

In [7]:

import plotly.express as px

df = px.data.stocks(datetimes=True)
fig = px.scatter(df, x="date", y="GOOG", trendline="lowess")
fig.show()

new in v5.2

The level of smoothing can be controlled via the frac trendline option, which indicates the fraction of the data that the LOWESS smoother should include. The default is a fairly smooth line with frac=0.6666 and lowering this fraction will give a line that more closely follows the data.

In [8]:

import plotly.express as px

df = px.data.stocks(datetimes=True)
fig = px.scatter(df, x="date", y="GOOG", trendline="lowess", trendline_options=dict(frac=0.1))
fig.show()

Moving Averages¶

new in v5.2

Plotly Express can leverage Pandas' rolling, ewm and expanding functions in trendlines as well, for example to display moving averages. Values passed to trendline_options are passed directly to the underlying Pandas function (with the exception of the function and function_options keys, see below).

In [9]:

import plotly.express as px

df = px.data.stocks(datetimes=True)
fig = px.scatter(df, x="date", y="GOOG", trendline="rolling", trendline_options=dict(window=5),
                title="5-point moving average")
fig.show()

In [10]:

import plotly.express as px

df = px.data.stocks(datetimes=True)
fig = px.scatter(df, x="date", y="GOOG", trendline="ewm", trendline_options=dict(halflife=2),
                title="Exponentially-weighted moving average (halflife of 2 points)")
fig.show()

In [11]:

import plotly.express as px

df = px.data.stocks(datetimes=True)
fig = px.scatter(df, x="date", y="GOOG", trendline="expanding", title="Expanding mean")
fig.show()

Other Functions¶

The rolling, expanding and ewm trendlines support other functions than the default mean, enabling, for example, a moving-median trendline, or an expanding-max trendline.

In [12]:

import plotly.express as px

df = px.data.stocks(datetimes=True)
fig = px.scatter(df, x="date", y="GOOG", trendline="rolling", trendline_options=dict(function="median", window=5),
                title="Rolling Median")
fig.show()

In [13]:

import plotly.express as px

df = px.data.stocks(datetimes=True)
fig = px.scatter(df, x="date", y="GOOG", trendline="expanding", trendline_options=dict(function="max"),
                title="Expanding Maximum")
fig.show()

In some cases, it is necessary to pass options into the underying Pandas function, for example the std parameter must be provided if the win_type argument to rolling is "gaussian". This is possible with the function_args trendline option.

In [14]:

import plotly.express as px

df = px.data.stocks(datetimes=True)
fig = px.scatter(df, x="date", y="GOOG", trendline="rolling", 
                 trendline_options=dict(window=5, win_type="gaussian", function_args=dict(std=2)),
                title="Rolling Mean with Gaussian Window")
fig.show()

Displaying only the trendlines¶

In some cases, it may be desirable to show only the trendlines, by removing the scatter points.

In [15]:

import plotly.express as px

df = px.data.stocks(indexed=True, datetimes=True)
fig = px.scatter(df, trendline="rolling", trendline_options=dict(window=5),
                title="5-point moving average")
fig.data = [t for t in fig.data if t.mode == "lines"]
fig.update_traces(showlegend=True) #trendlines have showlegend=False by default
fig.show()

In [ ]:

What About Dash?¶

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(...)
# fig.add_trace( ... )
# fig.update_layout( ... )

from dash import Dash, dcc, html

app = Dash()
app.layout = html.Div([
    dcc.Graph(figure=fig)
])

app.run_server(debug=True, use_reloader=False)  # Turn off reloader if inside Jupyter