Much of this is from the following source: https://onlinecourses.science.psu.edu/stat501/node/257

In [1]:
import numpy as np
import numpy.linalg as la
import matplotlib.pyplot as plt

# print(plt.style.available) # uncomment to print all styles
import seaborn as sns
sns.set(font_scale=2)
plt.style.use('seaborn-whitegrid')
plt.rcParams['figure.figsize'] = (12,6.0)
%matplotlib inline

import pandas as pd

from scipy import stats

Example 1: building stories vs height

In [2]:
data = pd.read_csv('./bldgstories.txt', delim_whitespace=True)
In [3]:
year = data.values[:,0]
hght = data.values[:,1]
stories= data.values[:,2]
In [4]:
plt.plot(hght, stories, 'o')
plt.xlabel('height')
plt.ylabel('stories')
Out[4]:
Text(0,0.5,'stories')

Add a linear regresssion line

This is of the form $$ a x + b $$ where $a$ is the slope and $b$ is the intercept.

In [5]:
a, b, rvalue, pvalue, stderr = stats.linregress(hght, stories)
yfit = a*hght + b
plt.plot(hght, yfit, 'r-')

plt.plot(hght, stories, 'o')
plt.xlabel('height')
plt.ylabel('stories')
Out[5]:
Text(0,0.5,'stories')

Now add a line representing the distance to the linear line

In [6]:
a, b, rvalue, pvalue, stderr = stats.linregress(hght, stories)
yfit = a*hght + b
plt.plot(hght, yfit, 'r-')


for i in range(len(hght)):
    x = hght[i]
    y = yfit[i]
    s = stories[i]
    plt.plot([x, x], [y, s], 'k-')

plt.plot(hght, stories, 'o')
plt.xlabel('height')
plt.ylabel('stories')
Out[6]:
Text(0,0.5,'stories')

How far away is each dot from the red line?

yfit is the straight line

stories is the data

If yfit-stories were 0, then this would be a perfect fit, meaning a strong correlation and a good fit with a line would be 100% (or 1.0).

rvalue or correlation coefficient.

In [8]:
rvalue
Out[8]:
0.95055489426277295

Example 2, eye sight distance vs age

In [7]:
data = pd.read_csv('./signdist.txt', delim_whitespace=True)
In [9]:
age = data.values[:,0]
distance = data.values[:,1]
In [12]:
a, b, rvalue, pvalue, stderr = stats.linregress(age, distance)
yfit = a*age + b
plt.plot(age, yfit, 'r-')


for i in range(len(age)):
    x = age[i]
    y = yfit[i]
    s = distance[i]
    plt.plot([x, x], [y, s], 'k-')

plt.plot(age, distance, 'o')
plt.xlabel('age')
plt.ylabel('distance')

print(abs(rvalue))

0.801244650941

Example 3, height vs GPA

What?!

In [17]:
data = pd.read_csv('./heightgpa.txt', delim_whitespace=True)
In [18]:
height = data.values[:,0]
gpa = data.values[:,1]
In [21]:
a, b, rvalue, pvalue, stderr = stats.linregress(height, gpa)
yfit = a*height + b
plt.plot(height, yfit, 'r-')


for i in range(len(height)):
    x = height[i]
    y = yfit[i]
    s = gpa[i]
    plt.plot([x, x], [y, s], 'k-')

plt.plot(height, gpa, 'o')
plt.xlabel('height')
plt.ylabel('gpa')

print(abs(rvalue))

0.0532412598869