# Exercise 2.10

%matplotlib inline

import pandas as pd
import seaborn as sns
import numpy as np
import matplotlib.pyplot as plt


### a) Dataset overview

In Python we can load the Boston dataset using scikit-learn.

from sklearn.datasets import load_boston

df = pd.DataFrame(boston.data, columns=boston.feature_names)
df['target'] = boston.target

print(boston['DESCR'])

Boston House Prices dataset
===========================

Notes
------
Data Set Characteristics:

:Number of Instances: 506

:Number of Attributes: 13 numeric/categorical predictive

:Median Value (attribute 14) is usually the target

:Attribute Information (in order):
- CRIM     per capita crime rate by town
- ZN       proportion of residential land zoned for lots over 25,000 sq.ft.
- INDUS    proportion of non-retail business acres per town
- CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)
- NOX      nitric oxides concentration (parts per 10 million)
- RM       average number of rooms per dwelling
- AGE      proportion of owner-occupied units built prior to 1940
- DIS      weighted distances to five Boston employment centres
- TAX      full-value property-tax rate per $10,000 - PTRATIO pupil-teacher ratio by town - B 1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town - LSTAT % lower status of the population - MEDV Median value of owner-occupied homes in$1000's

:Missing Attribute Values: None

:Creator: Harrison, D. and Rubinfeld, D.L.

This is a copy of UCI ML housing dataset.
http://archive.ics.uci.edu/ml/datasets/Housing

This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.

The Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic
prices and the demand for clean air', J. Environ. Economics & Management,
vol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics
...', Wiley, 1980.   N.B. Various transformations are used in the table on
pages 244-261 of the latter.

The Boston house-price data has been used in many machine learning papers that address regression
problems.

**References**

- Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.
- Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.
- many more! (see http://archive.ics.uci.edu/ml/datasets/Housing)

df.head()

CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX PTRATIO B LSTAT target
0 0.00632 18.0 2.31 0.0 0.538 6.575 65.2 4.0900 1.0 296.0 15.3 396.90 4.98 24.0
1 0.02731 0.0 7.07 0.0 0.469 6.421 78.9 4.9671 2.0 242.0 17.8 396.90 9.14 21.6
2 0.02729 0.0 7.07 0.0 0.469 7.185 61.1 4.9671 2.0 242.0 17.8 392.83 4.03 34.7
3 0.03237 0.0 2.18 0.0 0.458 6.998 45.8 6.0622 3.0 222.0 18.7 394.63 2.94 33.4
4 0.06905 0.0 2.18 0.0 0.458 7.147 54.2 6.0622 3.0 222.0 18.7 396.90 5.33 36.2
np.shape(df)

(506, 14)


Number of rows and columns 506 rows. 14 columns.

Rows and columns description Each rows is town in Boston area. Columns are features that can influence house price such as per capita crime rate by town ('CRIM').

### b) Scatterplots

• We'll use seaborn to get a quick overview of pairwise relationships
g = sns.PairGrid(df)
g.map_upper(plt.scatter, s=3)
g.map_diag(plt.hist)
g.map_lower(plt.scatter, s=3)
g.fig.set_size_inches(12, 12)


plt.scatter(df['RM'], df['target'])
plt.xlabel('RM')
plt.ylabel('target');


Findings It seems to exist a positive linear relationship between RM and target This is expected as RM is the number of rooms (more space, higher price)

plt.scatter(df['LSTAT'], df['target'])
plt.xlabel('LSTAT')
plt.ylabel('target');


Findings LSTAT and target seem to have a negative non-linear relationship This is expected as LSTAT is the percent of lower status people (lower status, lower incomes, cheaper houses)

plt.scatter(df['RM'], df['LSTAT'])
plt.xlabel('RM')
plt.ylabel('LSTAT');


Findings It seems to exist a negative non-linear relationship between LSTAT and RM It makes sense since people with less money (higher LSTAT) can't afford bigger houses (high RM)

### c) Predictors associated with capita crime rate

df.corrwith(df['CRIM']).sort_values()

target    -0.385832
DIS       -0.377904
B         -0.377365
RM        -0.219940
ZN        -0.199458
CHAS      -0.055295
PTRATIO    0.288250
AGE        0.350784
INDUS      0.404471
NOX        0.417521
LSTAT      0.452220
TAX        0.579564
CRIM       1.000000
dtype: float64


Looking at the previous scatterplots and the correlation of each variable with 'CRIM', we will have a closer at the 3 with the largest correlation, namely: RAD, index of accessibility to radial highways, TAX, full-value property-tax rate (in dollars per \$10,000), * LSTAT, percentage of lower status of the population.

ax = sns.boxplot(x="RAD", y="CRIM", data=df)


Findings * When RAD is equal to 24 (its highest value), average CRIM is much higher and CRIM range is much larger.

plt.scatter(df['TAX'], df['CRIM'])
plt.xlabel('TAX')
plt.ylabel('CRIM');


Findings * When TAX is equal to 666, average CRIM is much higher and CRIM range is much larger.

plt.scatter(df['LSTAT'], df['CRIM'])
plt.xlabel('LSTAT')
plt.ylabel('CRIM');


Findings For lower values of LSTAT (< 10), CRIM is always under 10. For LSTAT > 10, there is a wider spread of CRIM. For LSTAT < 20, a large proportion of the data points is very close to CRIM = 0.

### d) Crime rate, tax rate and pupil-teacher ratio in suburbs

df.ix[df['CRIM'].nlargest(5).index]

CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX PTRATIO B LSTAT target
380 88.9762 0.0 18.1 0.0 0.671 6.968 91.9 1.4165 24.0 666.0 20.2 396.90 17.21 10.4
418 73.5341 0.0 18.1 0.0 0.679 5.957 100.0 1.8026 24.0 666.0 20.2 16.45 20.62 8.8
405 67.9208 0.0 18.1 0.0 0.693 5.683 100.0 1.4254 24.0 666.0 20.2 384.97 22.98 5.0
410 51.1358 0.0 18.1 0.0 0.597 5.757 100.0 1.4130 24.0 666.0 20.2 2.60 10.11 15.0
414 45.7461 0.0 18.1 0.0 0.693 4.519 100.0 1.6582 24.0 666.0 20.2 88.27 36.98 7.0
df.ix[df['TAX'].nlargest(5).index]

CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX PTRATIO B LSTAT target
488 0.15086 0.0 27.74 0.0 0.609 5.454 92.7 1.8209 4.0 711.0 20.1 395.09 18.06 15.2
489 0.18337 0.0 27.74 0.0 0.609 5.414 98.3 1.7554 4.0 711.0 20.1 344.05 23.97 7.0
490 0.20746 0.0 27.74 0.0 0.609 5.093 98.0 1.8226 4.0 711.0 20.1 318.43 29.68 8.1
491 0.10574 0.0 27.74 0.0 0.609 5.983 98.8 1.8681 4.0 711.0 20.1 390.11 18.07 13.6
492 0.11132 0.0 27.74 0.0 0.609 5.983 83.5 2.1099 4.0 711.0 20.1 396.90 13.35 20.1
df.ix[df['PTRATIO'].nlargest(5).index]

CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX PTRATIO B LSTAT target
354 0.04301 80.0 1.91 0.0 0.413 5.663 21.9 10.5857 4.0 334.0 22.0 382.80 8.05 18.2
355 0.10659 80.0 1.91 0.0 0.413 5.936 19.5 10.5857 4.0 334.0 22.0 376.04 5.57 20.6
127 0.25915 0.0 21.89 0.0 0.624 5.693 96.0 1.7883 4.0 437.0 21.2 392.11 17.19 16.2
128 0.32543 0.0 21.89 0.0 0.624 6.431 98.8 1.8125 4.0 437.0 21.2 396.90 15.39 18.0
129 0.88125 0.0 21.89 0.0 0.624 5.637 94.7 1.9799 4.0 437.0 21.2 396.90 18.34 14.3
df.describe()

CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX PTRATIO B LSTAT target
count 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000
mean 3.593761 11.363636 11.136779 0.069170 0.554695 6.284634 68.574901 3.795043 9.549407 408.237154 18.455534 356.674032 12.653063 22.532806
std 8.596783 23.322453 6.860353 0.253994 0.115878 0.702617 28.148861 2.105710 8.707259 168.537116 2.164946 91.294864 7.141062 9.197104
min 0.006320 0.000000 0.460000 0.000000 0.385000 3.561000 2.900000 1.129600 1.000000 187.000000 12.600000 0.320000 1.730000 5.000000
25% 0.082045 0.000000 5.190000 0.000000 0.449000 5.885500 45.025000 2.100175 4.000000 279.000000 17.400000 375.377500 6.950000 17.025000
50% 0.256510 0.000000 9.690000 0.000000 0.538000 6.208500 77.500000 3.207450 5.000000 330.000000 19.050000 391.440000 11.360000 21.200000
75% 3.647423 12.500000 18.100000 0.000000 0.624000 6.623500 94.075000 5.188425 24.000000 666.000000 20.200000 396.225000 16.955000 25.000000
max 88.976200 100.000000 27.740000 1.000000 0.871000 8.780000 100.000000 12.126500 24.000000 711.000000 22.000000 396.900000 37.970000 50.000000

Findings The 5 towns shown in CRIM table are particularly high All the towns shown in the TAX table have maximum TAX level * PTRATIO table shows towns with high pupil-teacher ratios but not so uneven

### e) Suburbs bounding the Charles river

df['CHAS'].value_counts()[1]

35


### (f) Median pupil-teacher ratio

df['PTRATIO'].median()

19.05


### (g) Suburb with lowest median value of owner occupied homes

df['target'].idxmin()

398

a = df.describe()
a.loc['range'] = a.loc['max'] - a.loc['min']
a.loc[398] = df.ix[398]
a

CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX PTRATIO B LSTAT target
count 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000
mean 3.593761 11.363636 11.136779 0.069170 0.554695 6.284634 68.574901 3.795043 9.549407 408.237154 18.455534 356.674032 12.653063 22.532806
std 8.596783 23.322453 6.860353 0.253994 0.115878 0.702617 28.148861 2.105710 8.707259 168.537116 2.164946 91.294864 7.141062 9.197104
min 0.006320 0.000000 0.460000 0.000000 0.385000 3.561000 2.900000 1.129600 1.000000 187.000000 12.600000 0.320000 1.730000 5.000000
25% 0.082045 0.000000 5.190000 0.000000 0.449000 5.885500 45.025000 2.100175 4.000000 279.000000 17.400000 375.377500 6.950000 17.025000
50% 0.256510 0.000000 9.690000 0.000000 0.538000 6.208500 77.500000 3.207450 5.000000 330.000000 19.050000 391.440000 11.360000 21.200000
75% 3.647423 12.500000 18.100000 0.000000 0.624000 6.623500 94.075000 5.188425 24.000000 666.000000 20.200000 396.225000 16.955000 25.000000
max 88.976200 100.000000 27.740000 1.000000 0.871000 8.780000 100.000000 12.126500 24.000000 711.000000 22.000000 396.900000 37.970000 50.000000
range 88.969880 100.000000 27.280000 1.000000 0.486000 5.219000 97.100000 10.996900 23.000000 524.000000 9.400000 396.580000 36.240000 45.000000
398 38.351800 0.000000 18.100000 0.000000 0.693000 5.453000 100.000000 1.489600 24.000000 666.000000 20.200000 396.900000 30.590000 5.000000

Findings The suburb with the lowest median value is 398. Relative to the other towns, this suburb has high CRIM, ZN below quantile 75%, above mean INDUS, does not bound the Charles river, above mean NOX, RM below quantile 25%, maximum AGE, DIS near to the minimum value, maximum RAD, TAX in quantile 75%, PTRATIO as well, B maximum and LSTAT above quantile 75%.

### h) Number of rooms per dwelling

len(df[df['RM']>7])

64

len(df[df['RM']>8])

13

len(df[df['RM']>8])

13

df[df['RM']>8].describe()

CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX PTRATIO B LSTAT target
count 13.000000 13.000000 13.000000 13.000000 13.000000 13.000000 13.000000 13.000000 13.000000 13.000000 13.000000 13.000000 13.000000 13.000000
mean 0.718795 13.615385 7.078462 0.153846 0.539238 8.348538 71.538462 3.430192 7.461538 325.076923 16.361538 385.210769 4.310000 44.200000
std 0.901640 26.298094 5.392767 0.375534 0.092352 0.251261 24.608723 1.883955 5.332532 110.971063 2.410580 10.529359 1.373566 8.092383
min 0.020090 0.000000 2.680000 0.000000 0.416100 8.034000 8.400000 1.801000 2.000000 224.000000 13.000000 354.550000 2.470000 21.900000
25% 0.331470 0.000000 3.970000 0.000000 0.504000 8.247000 70.400000 2.288500 5.000000 264.000000 14.700000 384.540000 3.320000 41.700000
50% 0.520140 0.000000 6.200000 0.000000 0.507000 8.297000 78.300000 2.894400 7.000000 307.000000 17.400000 386.860000 4.140000 48.300000
75% 0.578340 20.000000 6.200000 0.000000 0.605000 8.398000 86.500000 3.651900 8.000000 307.000000 17.400000 389.700000 5.120000 50.000000
max 3.474280 95.000000 19.580000 1.000000 0.718000 8.780000 93.900000 8.906700 24.000000 666.000000 20.200000 396.900000 7.440000 50.000000
df.describe()

CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX PTRATIO B LSTAT target
count 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000
mean 3.593761 11.363636 11.136779 0.069170 0.554695 6.284634 68.574901 3.795043 9.549407 408.237154 18.455534 356.674032 12.653063 22.532806
std 8.596783 23.322453 6.860353 0.253994 0.115878 0.702617 28.148861 2.105710 8.707259 168.537116 2.164946 91.294864 7.141062 9.197104
min 0.006320 0.000000 0.460000 0.000000 0.385000 3.561000 2.900000 1.129600 1.000000 187.000000 12.600000 0.320000 1.730000 5.000000
25% 0.082045 0.000000 5.190000 0.000000 0.449000 5.885500 45.025000 2.100175 4.000000 279.000000 17.400000 375.377500 6.950000 17.025000
50% 0.256510 0.000000 9.690000 0.000000 0.538000 6.208500 77.500000 3.207450 5.000000 330.000000 19.050000 391.440000 11.360000 21.200000
75% 3.647423 12.500000 18.100000 0.000000 0.624000 6.623500 94.075000 5.188425 24.000000 666.000000 20.200000 396.225000 16.955000 25.000000
max 88.976200 100.000000 27.740000 1.000000 0.871000 8.780000 100.000000 12.126500 24.000000 711.000000 22.000000 396.900000 37.970000 50.000000

Comments CRIM is lower, INDUS proportion is lower, * % of lower status of the population (LSTAT) is lower.