This package is a reproduction of the summary.lm and plot.lm function in R but for a python environment and is meant to support the sklearn library by adding model summary and diagnostic plots for linear regression.
In the R environment, we can fit a linear model and generate a model summary and diagnostic plots by doing the following:
> fit = lm(y ~ ., data=data)
> summary(fit)
Call:
lm(formula = y ~ ., data = data)
Residuals:
Min 1Q Median 3Q Max
-155.829 -38.534 -0.227 37.806 151.355
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 152.133 2.576 59.061 < 2e-16 ***
X0 -10.012 59.749 -0.168 0.867000
X1 -239.819 61.222 -3.917 0.000104 ***
X2 519.840 66.534 7.813 4.30e-14 ***
X3 324.390 65.422 4.958 1.02e-06 ***
X4 -792.184 416.684 -1.901 0.057947 .
X5 476.746 339.035 1.406 0.160389
X6 101.045 212.533 0.475 0.634721
X7 177.064 161.476 1.097 0.273456
X8 751.279 171.902 4.370 1.56e-05 ***
X9 67.625 65.984 1.025 0.305998
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 54.15 on 431 degrees of freedom
Multiple R-squared: 0.5177, Adjusted R-squared: 0.5066
F-statistic: 46.27 on 10 and 431 DF, p-value: < 2.2e-16
> par(mfrow=c(2,3))
> plot(fit, which=1:6)
The goal of this package is to make this process as simple as it is in R for a sklearn LinearRegression object.
pip install pyplotlmThere are two core functionalities:
A. generate a R style regression model summary (R summary.lm)
B. plot six available diagnostic plots (R plot.lm):
1. Residuals vs Fitted
2. Normal Q-Q
3. Scale-Location
4. Cook's Distance
5. Residuals vs Leverage
6. Cook's Distance vs Leverage / (1-Leverage)
Below is how you would produce the summary and diagnostic plots in Python:
>>> from sklearn.datasets import load_diabetes
>>> from sklearn.linear_model import LinearRegression
>>> import matplotlib.pyplot as plt
>>> from pyplotlm import *
>>> X, y = load_diabetes(return_X_y=True)
>>> reg = LinearRegression().fit(X, y)
>>> obj = PyPlotLm(reg, X, y, intercept=False)
>>> obj.summary() # or summary(obj)
Residuals:
Min 1Q Median 3Q Max
-155.8290 -38.5339 -0.2269 37.8061 151.3550
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 152.1335 2.5759 59.0614 0.0000 ***
X0 -10.0122 59.7492 -0.1676 0.8670
X1 -239.8191 61.2223 -3.9172 0.0001 ***
X2 519.8398 66.5336 7.8132 0.0000 ***
X3 324.3904 65.4219 4.9584 0.0000 ***
X4 -792.1842 416.6839 -1.9012 0.0579 .
X5 476.7458 339.0345 1.4062 0.1604
X6 101.0446 212.5326 0.4754 0.6347
X7 177.0642 161.4756 1.0965 0.2735
X8 751.2793 171.9020 4.3704 0.0000 ***
X9 67.6254 65.9842 1.0249 0.3060
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 54.154 on 431 degrees of freedom
Multiple R-squared: 0.5177, Adjusted R-squared: 0.5066
F-statistic: 46.27 on 10 and 431 DF, p-value: 1.11e-16
>>> obj.plot(which='all') # or plot(obj, which='all')
>>> plt.show()
This will produce the same set of diagnostic plots:
-
Regression Deletion Diagnostics (R)
https://stat.ethz.ch/R-manual/R-devel/library/stats/html/influence.measures.html
https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/lm
https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/plot.lm -
Residuals and Influence in Regression
https://conservancy.umn.edu/handle/11299/37076
https://en.wikipedia.org/wiki/Leverage_(statistics)
https://en.wikipedia.org/wiki/Studentized_residual -
Cook's Distance
https://en.wikipedia.org/wiki/Cook%27s_distance