In [1]:
import pandas as pd
import numpy as np
from matplotlib.pyplot import subplots
In [2]:
data = pd.read_csv('family_heights.csv')
data.head(3)
Out[2]:
family father mother midparentHeight children childNum sex childHeight
0 1 78.5 67.0 75.43 4 1 male 73.2
1 1 78.5 67.0 75.43 4 2 female 69.2
2 1 78.5 67.0 75.43 4 3 female 69.0
In [3]:
coefficients = np.polyfit(data['midparentHeight'], data['childHeight'], 1)
coefficients
Out[3]:
array([ 0.6373609 , 22.63624055])
In [6]:
data1 = data.assign(regressionEstimate = coefficients[0]*data['midparentHeight'] + coefficients[1])
data1.head(10)
Out[6]:
family father mother midparentHeight children childNum sex childHeight regressionEstimate
0 1 78.5 67.0 75.43 4 1 male 73.2 70.712373
1 1 78.5 67.0 75.43 4 2 female 69.2 70.712373
2 1 78.5 67.0 75.43 4 3 female 69.0 70.712373
3 1 78.5 67.0 75.43 4 4 female 69.0 70.712373
4 2 75.5 66.5 73.66 4 1 male 73.5 69.584244
5 2 75.5 66.5 73.66 4 2 male 72.5 69.584244
6 2 75.5 66.5 73.66 4 3 female 65.5 69.584244
7 2 75.5 66.5 73.66 4 4 female 65.5 69.584244
8 3 75.0 64.0 72.06 2 1 male 71.0 68.564467
9 3 75.0 64.0 72.06 2 2 female 68.0 68.564467
In [7]:
data2 = data1.assign(residuals = data1['childHeight'] - data1['regressionEstimate'])
data2.head(5)
Out[7]:
family father mother midparentHeight children childNum sex childHeight regressionEstimate residuals
0 1 78.5 67.0 75.43 4 1 male 73.2 70.712373 2.487627
1 1 78.5 67.0 75.43 4 2 female 69.2 70.712373 -1.512373
2 1 78.5 67.0 75.43 4 3 female 69.0 70.712373 -1.712373
3 1 78.5 67.0 75.43 4 4 female 69.0 70.712373 -1.712373
4 2 75.5 66.5 73.66 4 1 male 73.5 69.584244 3.915756
In [11]:
fig, ax = subplots(figsize = (5, 5))
ax.scatter(data2['midparentHeight'], data2['residuals'])
ax.axhline(y=0, color='red', linewidth = 3);
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In [12]:
# We showed in class that the mean of the residuals equals 0. 
# Let us check this for the heights data
print('Mean of the residuals = ', data2['residuals'].mean())

Mean of the residuals =  -7.323002542212767e-14

Due to precision errors, the value does not come out to be exactly 0, but it is really close!

In [13]:
# We showed in class that the correlation between the predictor and the residuals is 0
# Let us check for the heights data
print('Correlation of midparentHeights and residuals = ', data2['midparentHeight'].corr(data2['residuals']))

Correlation of midparentHeights and residuals =  -1.3549018592547941e-15

Again, due to precision errors, the value does not come out to be exactly 0, but it is really close!

In [ ]: