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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 (LOWESS) trendlines to scatterplots in Python. Options for moving averages (rolling means) as well as exponentially-weighted and expanding functions.

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In [1]:

import plotly.express as px

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

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]:

Notes:

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

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()

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()

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()

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()

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()

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()

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

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