{"id":23195,"date":"2018-07-30T04:00:11","date_gmt":"2018-07-30T04:00:11","guid":{"rendered":"https:\/\/data-flair.training\/blogs\/?p=23195"},"modified":"2026-04-28T15:44:49","modified_gmt":"2026-04-28T10:14:49","slug":"python-linear-regression-chi-square-test","status":"publish","type":"post","link":"https:\/\/data-flair.training\/blogs\/python-linear-regression-chi-square-test\/","title":{"rendered":"Python Linear Regression | Chi-Square Test In Python"},"content":{"rendered":"

Today, in this Python tutorial<\/strong><\/a>, we will discuss Python Linear Regression and Chi-Square Test in Python. Moreover, we will understand the meaning of Linear Regression and Chi-Square in Python. Also, we will look at the Python Linear Regression Example and the Chi-square example.<\/p>\n

So, let’s start with Python Linear Regression.<\/p>\n

Python Linear Regression<\/h3>\n

Linear regression is a way to model the relationship that a scalar response(a dependent variable) has with explanatory variable(s)(independent variables). Depending on whether we have one or more explanatory variables, we term it simple linear regression<\/b> and multiple linear regression in Python<\/b>.<\/p>\n

Do you know about Python SciPy<\/a>?<\/strong><\/p>\n

To model relationships, we use linear predictor functions with unknown model parameters; we call these linear models in Python<\/em>.<\/p>\n

We will use Seaborn<\/em> to plot a Python linear regression here.<\/p>\n

a. Python Linear Regression\u00a0Example<\/h4>\n

Let\u2019s take a simple example of Python Linear Regression.<\/p>\n

>>> import seaborn as sn\r\n>>> import matplotlib.pyplot as plt\r\n>>> sn.set(color_codes=True)\r\n>>> tips=sn.load_dataset('tips')\r\n>>> ax=sn.regplot(x='total_bill',y='tip',data=tips)\r\n>>> plt.show()<\/pre>\n
\"Python<\/a>
Python Linear Regression Example<\/p><\/div>\n
b. How to Customize the Color in Python Linear Regression?<\/h4>\n
Now let\u2019s color it green.
\nHave a look at Python NumPy<\/a><\/strong><\/p>\n
>>> import numpy as np\r\n>>> np.random.seed(7)\r\n>>> mean,cov=[3,5],[(1.3,.8),(.8,1.1)]\r\n>>> x,y=np.random.multivariate_normal(mean,cov,77).T\r\n>>> ax=sn.regplot(x=x,y=y,color='g')\r\n>>> plt.show()<\/pre>\n
\"Python<\/a>
Customizing the colour in Linear regression in Python Programming Language<\/p><\/div>\n
c. Plotting with Pandas Series, Customizing Markers<\/h4>\n
Now, we\u2019ll use two Python Pandas<\/a><\/strong> Series to plot a linear regression.<\/p>\n
>>> import pandas as pd\r\n>>> x,y=pd.Series(x,name='x'),pd.Series(y,name='y')\r\n>>> ax=sn.regplot(x=x,y=y,marker='*')<\/pre>\n
\"Python<\/a>
Customizing the color in Python Linear regression<\/p><\/div>\n
d. Setting a Confidence Interval<\/h4>\n
To set the confidence interval, we use the ci parameter. The confidence interval is a range of values that makes it probable that a parameter\u2019s value lies within it.
\nLet’s discuss Python Heatmap<\/a><\/strong><\/p>\n
>>> ax=sn.regplot(x=x,y=y,ci=68)\r\n>>> plt.show()<\/pre>\n
\"Python<\/a>
Setting a Confidence Interval<\/p><\/div>\n
e. Adding Jitter<\/h4>\n
You can add some jitter in the x or y directions.<\/p>\n
>>> ax=sn.regplot(x='size',y='total_bill',data=tips,y_jitter=.1,color='g')\r\n>>> plt.show()<\/pre>\n
\"Python<\/a>
Adding Jitter in Python Linear Regression<\/p><\/div>\n
f. Plotting With a Continuous Variable Divided into Discrete Bins<\/h4>\n
Let’s revise the Python Charts<\/a><\/strong>
\nLet\u2019s create 5 bins and make the plot.<\/p>\n
>>> ax=sn.regplot(x=x,y=y,x_bins=5)\r\n>>> plt.show()<\/pre>\n
\"Python<\/a>
Plotting With a Continuous Variable Divided into Discrete Bins<\/p><\/div>\n
What is the Chi-Square Test?<\/strong><\/h3>\n
The chi-square test is used to assess the relationship between two categorical variables. It helps determine whether the distribution of sample categorical data matches an expected distribution.<\/p>\n
This is a statistical hypothesis test that uses a chi-squared distribution as a sampling distribution for the test statistic when we have a true null hypothesis. In other words, it is a way to assess how a set of observed values fits in with the values expected in theory- the goodness of fit.<\/span><\/p>\n
The test tells us whether, in one or more categories, the expected frequencies differ significantly from the observed frequencies. We also write it as the <\/span>\u03c7<\/i><\/b>2<\/b> test. In this test, we classify observations into mutually exclusive classes. A null hypothesis tells us how probable it is that an observation falls into the corresponding class. With this test, we aim to determine how likely an observation is, while assuming that the null hypothesis is true. This Chi-Square test tells us whether two categorical variables depend on each other.<\/span><\/p>\n
a. Python Chi-Square Example<\/strong><\/h4>\n
Let\u2019s take an example.<\/span><\/p>\n
>>> from scipy import stats\r\n>>> import numpy as np\r\n>>> import matplotlib.pyplot as plt\r\n>>> x=np.linspace(0,10,100)\r\n>>> fig,ax=plt.subplots(1,1)\r\n>>> linestyles=['--','-.',':','-']\r\n>>> degrees_of_freedom=[1,3,7,5]\r\n>>> for df,ls in zip(degrees_of_freedom,linestyles):\r\n                ax.plot(x,stats.chi2.pdf(x,df),linestyle=ls) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><\/pre>\n
[<matplotlib.lines.Line2D object at 0x060314D0>]<\/strong>
\n[<matplotlib.lines.Line2D object at 0x06031590>]<\/strong>
\n[<matplotlib.lines.Line2D object at 0x060318B0>]<\/strong>
\n[<matplotlib.lines.Line2D object at 0x06031B50>]<\/strong><\/p>\n
>>> plt.xlim(0,7)<\/pre>\n
(0, 7)<\/strong><\/p>\n
>>> plt.ylim(0,0.5)<\/pre>\n
(0, 0.5)<\/strong>
\nLet’s discuss Python Compilers<\/a><\/strong><\/p>\n
>>> plt.show()<\/pre>\n
This code plots four line plots for us-<\/span><\/p>\n
\"Python<\/a>
Python Chi-Square Example<\/p><\/div>\n
b. scipy.stats.chisquare<\/strong><\/h4>\n
This calculates a one-way chi-square test for us. It has the following syntax-<\/span><\/p>\n
scipy.stats.chisquare(f_obs,f_exp=None,ddof=0,axis=0)<\/pre>\n
Consider the null hypothesis that the categorical data in question has the given frequencies. The Chi-square test tests this.<\/span>
\nIt has the following parameters-<\/span><\/p>\n