Chapter 2

Exercise 8

import numpy as np 

import pandas as pd
import matplotlib.pyplot as plt
from ISLP import load_data
from matplotlib.pyplot import subplots

---------------------------------------------------------------------------

ModuleNotFoundError                       Traceback (most recent call last)

Cell In[4], line 5

      3 import pandas as pd

      4 import matplotlib.pyplot as plt

----> 5 from ISLP import load_data

      6 from matplotlib.pyplot import subplots



ModuleNotFoundError: No module named 'ISLP'

(a)

college=pd.read_csv('College.csv')

---------------------------------------------------------------------------

FileNotFoundError                         Traceback (most recent call last)

Cell In[5], line 1

----> 1 college=pd.read_csv('College.csv')



File ~\AppData\Roaming\Python\Python313\site-packages\pandas\io\parsers\readers.py:1026, in read_csv(filepath_or_buffer, sep, delimiter, header, names, index_col, usecols, dtype, engine, converters, true_values, false_values, skipinitialspace, skiprows, skipfooter, nrows, na_values, keep_default_na, na_filter, verbose, skip_blank_lines, parse_dates, infer_datetime_format, keep_date_col, date_parser, date_format, dayfirst, cache_dates, iterator, chunksize, compression, thousands, decimal, lineterminator, quotechar, quoting, doublequote, escapechar, comment, encoding, encoding_errors, dialect, on_bad_lines, delim_whitespace, low_memory, memory_map, float_precision, storage_options, dtype_backend)

   1013 kwds_defaults = _refine_defaults_read(

   1014     dialect,

   1015     delimiter,

   (...)

   1022     dtype_backend=dtype_backend,

   1023 )

   1024 kwds.update(kwds_defaults)

-> 1026 return _read(filepath_or_buffer, kwds)



File ~\AppData\Roaming\Python\Python313\site-packages\pandas\io\parsers\readers.py:620, in _read(filepath_or_buffer, kwds)

    617 _validate_names(kwds.get("names", None))

    619 # Create the parser.

--> 620 parser = TextFileReader(filepath_or_buffer, **kwds)

    622 if chunksize or iterator:

    623     return parser



File ~\AppData\Roaming\Python\Python313\site-packages\pandas\io\parsers\readers.py:1620, in TextFileReader.__init__(self, f, engine, **kwds)

   1617     self.options["has_index_names"] = kwds["has_index_names"]

   1619 self.handles: IOHandles | None = None

-> 1620 self._engine = self._make_engine(f, self.engine)



File ~\AppData\Roaming\Python\Python313\site-packages\pandas\io\parsers\readers.py:1880, in TextFileReader._make_engine(self, f, engine)

   1878     if "b" not in mode:

   1879         mode += "b"

-> 1880 self.handles = get_handle(

   1881     f,

   1882     mode,

   1883     encoding=self.options.get("encoding", None),

   1884     compression=self.options.get("compression", None),

   1885     memory_map=self.options.get("memory_map", False),

   1886     is_text=is_text,

   1887     errors=self.options.get("encoding_errors", "strict"),

   1888     storage_options=self.options.get("storage_options", None),

   1889 )

   1890 assert self.handles is not None

   1891 f = self.handles.handle



File ~\AppData\Roaming\Python\Python313\site-packages\pandas\io\common.py:873, in get_handle(path_or_buf, mode, encoding, compression, memory_map, is_text, errors, storage_options)

    868 elif isinstance(handle, str):

    869     # Check whether the filename is to be opened in binary mode.

    870     # Binary mode does not support 'encoding' and 'newline'.

    871     if ioargs.encoding and "b" not in ioargs.mode:

    872         # Encoding

--> 873         handle = open(

    874             handle,

    875             ioargs.mode,

    876             encoding=ioargs.encoding,

    877             errors=errors,

    878             newline="",

    879         )

    880     else:

    881         # Binary mode

    882         handle = open(handle, ioargs.mode)



FileNotFoundError: [Errno 2] No such file or directory: 'College.csv'

(b)

college.head()

	Unnamed: 0	Private	Apps	Accept	Enroll	Top10perc	Top25perc	F.Undergrad	P.Undergrad	Outstate	Room.Board	Books	Personal	PhD	Terminal	S.F.Ratio	perc.alumni	Expend	Grad.Rate
0	Abilene Christian University	Yes	1660	1232	721	23	52	2885	537	7440	3300	450	2200	70	78	18.1	12	7041	60
1	Adelphi University	Yes	2186	1924	512	16	29	2683	1227	12280	6450	750	1500	29	30	12.2	16	10527	56
2	Adrian College	Yes	1428	1097	336	22	50	1036	99	11250	3750	400	1165	53	66	12.9	30	8735	54
3	Agnes Scott College	Yes	417	349	137	60	89	510	63	12960	5450	450	875	92	97	7.7	37	19016	59
4	Alaska Pacific University	Yes	193	146	55	16	44	249	869	7560	4120	800	1500	76	72	11.9	2	10922	15

college2 = pd.read_csv('College.csv', index_col =0)
college3 = college.rename({'Unnamed: 0': 'College'},axis=1)
college3 = college3.set_index('College')

college=college3

college.head()

	Private	Apps	Accept	Enroll	Top10perc	Top25perc	F.Undergrad	P.Undergrad	Outstate	Room.Board	Books	Personal	PhD	Terminal	S.F.Ratio	perc.alumni	Expend	Grad.Rate
College
Abilene Christian University	Yes	1660	1232	721	23	52	2885	537	7440	3300	450	2200	70	78	18.1	12	7041	60
Adelphi University	Yes	2186	1924	512	16	29	2683	1227	12280	6450	750	1500	29	30	12.2	16	10527	56
Adrian College	Yes	1428	1097	336	22	50	1036	99	11250	3750	400	1165	53	66	12.9	30	8735	54
Agnes Scott College	Yes	417	349	137	60	89	510	63	12960	5450	450	875	92	97	7.7	37	19016	59
Alaska Pacific University	Yes	193	146	55	16	44	249	869	7560	4120	800	1500	76	72	11.9	2	10922	15

(c)

college.describe()

	Apps	Accept	Enroll	Top10perc	Top25perc	F.Undergrad	P.Undergrad	Outstate	Room.Board	Books	Personal	PhD	Terminal	S.F.Ratio	perc.alumni	Expend	Grad.Rate
count	777.000000	777.000000	777.000000	777.000000	777.000000	777.000000	777.000000	777.000000	777.000000	777.000000	777.000000	777.000000	777.000000	777.000000	777.000000	777.000000	777.00000
mean	3001.638353	2018.804376	779.972973	27.558559	55.796654	3699.907336	855.298584	10440.669241	4357.526384	549.380952	1340.642214	72.660232	79.702703	14.089704	22.743887	9660.171171	65.46332
std	3870.201484	2451.113971	929.176190	17.640364	19.804778	4850.420531	1522.431887	4023.016484	1096.696416	165.105360	677.071454	16.328155	14.722359	3.958349	12.391801	5221.768440	17.17771
min	81.000000	72.000000	35.000000	1.000000	9.000000	139.000000	1.000000	2340.000000	1780.000000	96.000000	250.000000	8.000000	24.000000	2.500000	0.000000	3186.000000	10.00000
25%	776.000000	604.000000	242.000000	15.000000	41.000000	992.000000	95.000000	7320.000000	3597.000000	470.000000	850.000000	62.000000	71.000000	11.500000	13.000000	6751.000000	53.00000
50%	1558.000000	1110.000000	434.000000	23.000000	54.000000	1707.000000	353.000000	9990.000000	4200.000000	500.000000	1200.000000	75.000000	82.000000	13.600000	21.000000	8377.000000	65.00000
75%	3624.000000	2424.000000	902.000000	35.000000	69.000000	4005.000000	967.000000	12925.000000	5050.000000	600.000000	1700.000000	85.000000	92.000000	16.500000	31.000000	10830.000000	78.00000
max	48094.000000	26330.000000	6392.000000	96.000000	100.000000	31643.000000	21836.000000	21700.000000	8124.000000	2340.000000	6800.000000	103.000000	100.000000	39.800000	64.000000	56233.000000	118.00000

(d)

pd.plotting.scatter_matrix(college[['Top10perc','Apps','Enroll']]);

(e)

fig, ax = subplots(figsize=(8, 8))
college.boxplot('Outstate', by='Private', ax=ax);

(f)

college['Elite'] = pd.cut(college['Top10perc'],bins=2,labels=['No','Yes'])
#The exact formula provided by the exercise instructions did not work. In fact many observations 
#remained void.

college.value_counts(college['Elite'])

Elite
No     687
Yes     90
dtype: int64

fig, ax = subplots(figsize=(8, 8))
college.boxplot('Outstate', by='Elite', ax=ax);

(g)

fig, axes =plt.subplots(nrows=2,ncols= 2,figsize=(12,12))
college['Apps'].plot.hist(ax=axes[0,0])
college['Accept'].plot.hist(ax=axes[0,1])
college['Enroll'].plot.hist(ax=axes[1,0])
college['Outstate'].plot.hist(ax=axes[1,1]);
# We can create bins for each of the plotted columns

(h)

First off, let’s explore the type of each of the data set features. We can use the info() fiunction for this.

college.info()

<class 'pandas.core.frame.DataFrame'>
Index: 777 entries, Abilene Christian University to York College of Pennsylvania
Data columns (total 19 columns):
 #   Column       Non-Null Count  Dtype   
---  ------       --------------  -----   
 0   Private      777 non-null    object  
 1   Apps         777 non-null    int64   
 2   Accept       777 non-null    int64   
 3   Enroll       777 non-null    int64   
 4   Top10perc    777 non-null    int64   
 5   Top25perc    777 non-null    int64   
 6   F.Undergrad  777 non-null    int64   
 7   P.Undergrad  777 non-null    int64   
 8   Outstate     777 non-null    int64   
 9   Room.Board   777 non-null    int64   
 10  Books        777 non-null    int64   
 11  Personal     777 non-null    int64   
 12  PhD          777 non-null    int64   
 13  Terminal     777 non-null    int64   
 14  S.F.Ratio    777 non-null    float64 
 15  perc.alumni  777 non-null    int64   
 16  Expend       777 non-null    int64   
 17  Grad.Rate    777 non-null    int64   
 18  Elite        777 non-null    category
dtypes: category(1), float64(1), int64(16), object(1)
memory usage: 116.2+ KB

The whole features pertain to numerical type except for ‘Elite’ and ‘Private’. Note that it is preferred to convert Private to ‘category’ type instead of object in order to avoid potential errors when using this feature in a determined function.

college['Private']=college['Private'].astype('category')

We define three possible segments for the data set: - ‘Faculty’ : this segment comprises all the features which relate to faculty. This includes features ‘PhD’, ‘Terminal’ and ‘S.F.Ratio’; - ‘Students’: This segment includes the features which interests the students. It includes the following features: ‘Apps’, ‘Accept’, ‘Enroll’, ‘Top10perc’, ‘Top25perc’, ‘F.Undergrad’, ‘P.Undergrad’ and ‘Grad.Rate’; - ‘Finance’ : This segment includes the features which give insight about the business model of the university. It encompasses the following features: ‘Private’, ‘Outstate’, ‘Room.Board’, ‘Books’, ‘Personal’, ‘perc.alumni’ and ‘Expend’.

A university might be interested in the number of enrolled students every year as the dependent variable. This could be a good indicator of performance about the popularity of the university. We choose to focus univariate analysis from this perspective.

Our expectations related to Outstate tuition are the following: - The dependent variable msut be related to both Top10per et Top25perc - Attribute F.Undergrad play for sure an important role in the dependent variable prediction. - Attributes Apps and Accept must also be related to Enroll, since potential students will tend to apply more where they could be accepted and the enrollment numbers must then be at high levels. Let’s now check these hypotheses by drawing scatterplots.

pd.plotting.scatter_matrix(college[['Enroll','F.Undergrad','Top10perc','Top25perc','Accept',
                                    'Apps','Outstate']]);

As expected, Enroll looks positively correlated with Accept, F.Undergrad and Apps. However, the relationships with the other attributes look less evident. We should then focus on those three features as independent variables.

college.corr()

C:\Users\kabousselham\AppData\Local\Temp\ipykernel_17648\2850033496.py:1: FutureWarning: The default value of numeric_only in DataFrame.corr is deprecated. In a future version, it will default to False. Select only valid columns or specify the value of numeric_only to silence this warning.
  college.corr()

	Apps	Accept	Enroll	Top10perc	Top25perc	F.Undergrad	P.Undergrad	Outstate	Room.Board	Books	Personal	PhD	Terminal	S.F.Ratio	perc.alumni	Expend	Grad.Rate
Apps	1.000000	0.943451	0.846822	0.338834	0.351640	0.814491	0.398264	0.050159	0.164939	0.132559	0.178731	0.390697	0.369491	0.095633	-0.090226	0.259592	0.146755
Accept	0.943451	1.000000	0.911637	0.192447	0.247476	0.874223	0.441271	-0.025755	0.090899	0.113525	0.200989	0.355758	0.337583	0.176229	-0.159990	0.124717	0.067313
Enroll	0.846822	0.911637	1.000000	0.181294	0.226745	0.964640	0.513069	-0.155477	-0.040232	0.112711	0.280929	0.331469	0.308274	0.237271	-0.180794	0.064169	-0.022341
Top10perc	0.338834	0.192447	0.181294	1.000000	0.891995	0.141289	-0.105356	0.562331	0.371480	0.118858	-0.093316	0.531828	0.491135	-0.384875	0.455485	0.660913	0.494989
Top25perc	0.351640	0.247476	0.226745	0.891995	1.000000	0.199445	-0.053577	0.489394	0.331490	0.115527	-0.080810	0.545862	0.524749	-0.294629	0.417864	0.527447	0.477281
F.Undergrad	0.814491	0.874223	0.964640	0.141289	0.199445	1.000000	0.570512	-0.215742	-0.068890	0.115550	0.317200	0.318337	0.300019	0.279703	-0.229462	0.018652	-0.078773
P.Undergrad	0.398264	0.441271	0.513069	-0.105356	-0.053577	0.570512	1.000000	-0.253512	-0.061326	0.081200	0.319882	0.149114	0.141904	0.232531	-0.280792	-0.083568	-0.257001
Outstate	0.050159	-0.025755	-0.155477	0.562331	0.489394	-0.215742	-0.253512	1.000000	0.654256	0.038855	-0.299087	0.382982	0.407983	-0.554821	0.566262	0.672779	0.571290
Room.Board	0.164939	0.090899	-0.040232	0.371480	0.331490	-0.068890	-0.061326	0.654256	1.000000	0.127963	-0.199428	0.329202	0.374540	-0.362628	0.272363	0.501739	0.424942
Books	0.132559	0.113525	0.112711	0.118858	0.115527	0.115550	0.081200	0.038855	0.127963	1.000000	0.179295	0.026906	0.099955	-0.031929	-0.040208	0.112409	0.001061
Personal	0.178731	0.200989	0.280929	-0.093316	-0.080810	0.317200	0.319882	-0.299087	-0.199428	0.179295	1.000000	-0.010936	-0.030613	0.136345	-0.285968	-0.097892	-0.269344
PhD	0.390697	0.355758	0.331469	0.531828	0.545862	0.318337	0.149114	0.382982	0.329202	0.026906	-0.010936	1.000000	0.849587	-0.130530	0.249009	0.432762	0.305038
Terminal	0.369491	0.337583	0.308274	0.491135	0.524749	0.300019	0.141904	0.407983	0.374540	0.099955	-0.030613	0.849587	1.000000	-0.160104	0.267130	0.438799	0.289527
S.F.Ratio	0.095633	0.176229	0.237271	-0.384875	-0.294629	0.279703	0.232531	-0.554821	-0.362628	-0.031929	0.136345	-0.130530	-0.160104	1.000000	-0.402929	-0.583832	-0.306710
perc.alumni	-0.090226	-0.159990	-0.180794	0.455485	0.417864	-0.229462	-0.280792	0.566262	0.272363	-0.040208	-0.285968	0.249009	0.267130	-0.402929	1.000000	0.417712	0.490898
Expend	0.259592	0.124717	0.064169	0.660913	0.527447	0.018652	-0.083568	0.672779	0.501739	0.112409	-0.097892	0.432762	0.438799	-0.583832	0.417712	1.000000	0.390343
Grad.Rate	0.146755	0.067313	-0.022341	0.494989	0.477281	-0.078773	-0.257001	0.571290	0.424942	0.001061	-0.269344	0.305038	0.289527	-0.306710	0.490898	0.390343	1.000000

Both correlation matrix and scatterplots show that ‘Apps’, ‘F.Undergrad’ and ‘Accept’ are twin brothers. We should choose one of them and let it be ‘Accept’. We could also argue that there is a nonlinear relationship between the dependent variable and ‘Outstate’. The same thing could be noticed with ‘Top10perc’.

Our choice finally lands on ‘Accept’, ‘Outstate’ and ‘Top10perc’ as independent variables.

Hopefully there are no missing data as we can notice from previous outputs. The data set contains 777 entries and all the features show the same count of inputs.

Now let’s look for outliars. Unfortunately the process of finding outliers can be tieresome and not adapted to the question instruction. The process intails dectecting potential outliers using univariate, bivariate and multivariate analysis accross the whole data set, then trying to classify each potential outlier and spot the variable or the reasons behind it.
Consequently, we assume here that there is no aberrant outlier among all the potential ones. Hence, in order to preserve the generalizability of the population features they must all be retained.

Instead of searching outliars we check below whether there are inconsistant observations. The inconsistency can be found by comparing the triplet’Apps’, ‘Accept’ and ‘Enroll’ for each observation.
In fact, for every university the number of applications should logically be greater than number of accepted students which in turn should be greater than the number of students enrolled.
Below we discover that such inconsistencies does not exist in the data set.

college.loc[lambda college:college['Apps']<college['Accept']].count()

Private        0
Apps           0
Accept         0
Enroll         0
Top10perc      0
Top25perc      0
F.Undergrad    0
P.Undergrad    0
Outstate       0
Room.Board     0
Books          0
Personal       0
PhD            0
Terminal       0
S.F.Ratio      0
perc.alumni    0
Expend         0
Grad.Rate      0
Elite          0
standard       0
dtype: int64

college.loc[lambda college:college['Accept']<college['Enroll']].count()

Private        0
Apps           0
Accept         0
Enroll         0
Top10perc      0
Top25perc      0
F.Undergrad    0
P.Undergrad    0
Outstate       0
Room.Board     0
Books          0
Personal       0
PhD            0
Terminal       0
S.F.Ratio      0
perc.alumni    0
Expend         0
Grad.Rate      0
Elite          0
standard       0
dtype: int64

Further exploration can be left to the reader. Next steps can include the verfication of normality, homoscedasticity, correlated errors and linearty.
The interested reader can find more in the following references: - Data Preparation for Machine Learning Data Cleaning, Feature Selection, and Data Transforms in Python by Jason Brownlee; - Multivariate Data Analysis by Joseph F. Hair et al., 8th edition.

Exercise 9

Auto=load_data('Auto')

Auto.columns

Index(['mpg', 'cylinders', 'displacement', 'horsepower', 'weight',
       'acceleration', 'year', 'origin', 'name'],
      dtype='object')

for col in Auto.columns:
    template = 'Column "{0}" has {1} missing values'
    print(template.format(col,pd.isnull(Auto[col]).sum()))

Column "mpg" has 0 missing values
Column "cylinders" has 0 missing values
Column "displacement" has 0 missing values
Column "horsepower" has 0 missing values
Column "weight" has 0 missing values
Column "acceleration" has 0 missing values
Column "year" has 0 missing values
Column "origin" has 0 missing values
Column "name" has 0 missing values

There is no missing value in the data set.

(a)

Auto.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 392 entries, 0 to 391
Data columns (total 9 columns):
 #   Column        Non-Null Count  Dtype  
---  ------        --------------  -----  
 0   mpg           392 non-null    float64
 1   cylinders     392 non-null    int64  
 2   displacement  392 non-null    float64
 3   horsepower    392 non-null    int64  
 4   weight        392 non-null    int64  
 5   acceleration  392 non-null    float64
 6   year          392 non-null    int64  
 7   origin        392 non-null    int64  
 8   name          392 non-null    object 
dtypes: float64(3), int64(5), object(1)
memory usage: 27.7+ KB

All predictors are quantitative except for the ‘name’ feature.

(b) and (c)

#The method describe() does the job automatically for all quantitative columns
Auto.describe()

	mpg	cylinders	displacement	horsepower	weight	acceleration	year	origin
count	392.000000	392.000000	392.000000	392.000000	392.000000	392.000000	392.000000	392.000000
mean	23.445918	5.471939	194.411990	104.469388	2977.584184	15.541327	75.979592	1.576531
std	7.805007	1.705783	104.644004	38.491160	849.402560	2.758864	3.683737	0.805518
min	9.000000	3.000000	68.000000	46.000000	1613.000000	8.000000	70.000000	1.000000
25%	17.000000	4.000000	105.000000	75.000000	2225.250000	13.775000	73.000000	1.000000
50%	22.750000	4.000000	151.000000	93.500000	2803.500000	15.500000	76.000000	1.000000
75%	29.000000	8.000000	275.750000	126.000000	3614.750000	17.025000	79.000000	2.000000
max	46.600000	8.000000	455.000000	230.000000	5140.000000	24.800000	82.000000	3.000000

(d)

Auto_b=Auto.drop(Auto.index[10:85])
Auto_b.describe()

	mpg	cylinders	displacement	horsepower	weight	acceleration	year	origin
count	317.000000	317.000000	317.000000	317.000000	317.000000	317.000000	317.000000	317.000000
mean	24.374763	5.381703	187.880126	101.003155	2938.854890	15.704101	77.123028	1.599369
std	7.872565	1.658135	100.169973	36.003208	811.640668	2.719913	3.127158	0.819308
min	11.000000	3.000000	68.000000	46.000000	1649.000000	8.500000	70.000000	1.000000
25%	18.000000	4.000000	101.000000	75.000000	2215.000000	14.000000	75.000000	1.000000
50%	23.900000	4.000000	146.000000	90.000000	2795.000000	15.500000	77.000000	1.000000
75%	30.500000	6.000000	250.000000	115.000000	3520.000000	17.300000	80.000000	2.000000
max	46.600000	8.000000	455.000000	230.000000	4997.000000	24.800000	82.000000	3.000000

Differences are noticeable between both previous tables.

(e)

pd.plotting.scatter_matrix(Auto,figsize=(12,12));

From the previous scatter plot we can draw the following preliminary conclusions:
- While acceleration envokes a normal distribution, both weight and mpg show flat tails like normal distribution and skewness; - The couples (displacement,weight), (horsepower, weight) and (horsepower, displacement) show strong linear relationships; - The couples (mpg,weight), (horsepower, mpg) and (mpg, displacement) show non-linear relationships.

(f)

Based on the conclusions of the previous question, we elect the features ‘weight’, ‘horsepower’ and ‘displacement’ as to be predictors of ‘mpg’. Further investigations must be done to find the best model and evaluate whether the interlying relationships are significant.

Exercise 10

(a)

Boston=load_data('Boston')

(b)

Boston.shape

(506, 13)

The previous instruction shows that Boston data set contains 506 lines and 13 columns.
Each row is a town in Boston area. Columns are factors which can influence house prices.

(c)

pd.plotting.scatter_matrix(Boston,figsize=(12,12));

From the previous scatter plot we can draw the following preliminary conclusions:
- While rm and medv probably stem from a normal distribution, features like dis, age, lstat, zn and crim may need transformations to satisfy normality; - The couple (rm, medv) shows a strong linear positive relationship; - The couple (rm,lstat) shows a negative non-linear relationship.

(d)

Boston.corrwith(Boston['crim'])

crim       1.000000
zn        -0.200469
indus      0.406583
chas      -0.055892
nox        0.420972
rm        -0.219247
age        0.352734
dis       -0.379670
rad        0.625505
tax        0.582764
ptratio    0.289946
lstat      0.455621
medv      -0.388305
dtype: float64

Most important correlations with ‘crim’ feature are discovered with both ‘rad’ and ‘tax’ features.
As per ’rad the adapted visualization is a boxplot, since this predictor take discrete values.

#Boxplot of crim by rad
fig, ax = subplots(figsize=(8, 8))
Boston.boxplot('crim', by='rad', ax=ax);

When the index of accessibility to radial highways is at the max (rad=24), the crime per capita rate is much higher both for median value and range.

#Boxplot of crim by tax
plt.scatter(Boston['tax'], Boston['crim']);

Boston['tax'].iloc[Boston['crim'].argmax()]

666

When the taxe rate is high (tax=666) the crime rate per capita reaches the max value as well as the largest range.

(e)

#Top ten suburbs with high crime rate
Boston.iloc[Boston['crim'].nlargest(10).index]

	crim	zn	indus	chas	nox	rm	age	dis	rad	tax	ptratio	lstat	medv
380	88.9762	0.0	18.1	0	0.671	6.968	91.9	1.4165	24	666	20.2	17.21	10.4
418	73.5341	0.0	18.1	0	0.679	5.957	100.0	1.8026	24	666	20.2	20.62	8.8
405	67.9208	0.0	18.1	0	0.693	5.683	100.0	1.4254	24	666	20.2	22.98	5.0
410	51.1358	0.0	18.1	0	0.597	5.757	100.0	1.4130	24	666	20.2	10.11	15.0
414	45.7461	0.0	18.1	0	0.693	4.519	100.0	1.6582	24	666	20.2	36.98	7.0
404	41.5292	0.0	18.1	0	0.693	5.531	85.4	1.6074	24	666	20.2	27.38	8.5
398	38.3518	0.0	18.1	0	0.693	5.453	100.0	1.4896	24	666	20.2	30.59	5.0
427	37.6619	0.0	18.1	0	0.679	6.202	78.7	1.8629	24	666	20.2	14.52	10.9
413	28.6558	0.0	18.1	0	0.597	5.155	100.0	1.5894	24	666	20.2	20.08	16.3
417	25.9406	0.0	18.1	0	0.679	5.304	89.1	1.6475	24	666	20.2	26.64	10.4

The top 10 suburbs with crime rate all have a taxe rate of 666 and a ptratio of 20.2

#Top ten suburbs with high tax rate
Boston.iloc[Boston['tax'].nlargest(10).index]

	crim	zn	indus	chas	nox	rm	age	dis	rad	tax	ptratio	lstat	medv
488	0.15086	0.0	27.74	0	0.609	5.454	92.7	1.8209	4	711	20.1	18.06	15.2
489	0.18337	0.0	27.74	0	0.609	5.414	98.3	1.7554	4	711	20.1	23.97	7.0
490	0.20746	0.0	27.74	0	0.609	5.093	98.0	1.8226	4	711	20.1	29.68	8.1
491	0.10574	0.0	27.74	0	0.609	5.983	98.8	1.8681	4	711	20.1	18.07	13.6
492	0.11132	0.0	27.74	0	0.609	5.983	83.5	2.1099	4	711	20.1	13.35	20.1
356	8.98296	0.0	18.10	1	0.770	6.212	97.4	2.1222	24	666	20.2	17.60	17.8
357	3.84970	0.0	18.10	1	0.770	6.395	91.0	2.5052	24	666	20.2	13.27	21.7
358	5.20177	0.0	18.10	1	0.770	6.127	83.4	2.7227	24	666	20.2	11.48	22.7
359	4.26131	0.0	18.10	0	0.770	6.112	81.3	2.5091	24	666	20.2	12.67	22.6
360	4.54192	0.0	18.10	0	0.770	6.398	88.0	2.5182	24	666	20.2	7.79	25.0

The top 10 suburbs with tax rate all have a particularly high ptratio between 20.1 and 20.2

#Top ten suburbs with high tax rate
Boston.iloc[Boston['ptratio'].nlargest(10).index]

	crim	zn	indus	chas	nox	rm	age	dis	rad	tax	ptratio	lstat	medv
354	0.04301	80.0	1.91	0	0.413	5.663	21.9	10.5857	4	334	22.0	8.05	18.2
355	0.10659	80.0	1.91	0	0.413	5.936	19.5	10.5857	4	334	22.0	5.57	20.6
127	0.25915	0.0	21.89	0	0.624	5.693	96.0	1.7883	4	437	21.2	17.19	16.2
128	0.32543	0.0	21.89	0	0.624	6.431	98.8	1.8125	4	437	21.2	15.39	18.0
129	0.88125	0.0	21.89	0	0.624	5.637	94.7	1.9799	4	437	21.2	18.34	14.3
130	0.34006	0.0	21.89	0	0.624	6.458	98.9	2.1185	4	437	21.2	12.60	19.2
131	1.19294	0.0	21.89	0	0.624	6.326	97.7	2.2710	4	437	21.2	12.26	19.6
132	0.59005	0.0	21.89	0	0.624	6.372	97.9	2.3274	4	437	21.2	11.12	23.0
133	0.32982	0.0	21.89	0	0.624	5.822	95.4	2.4699	4	437	21.2	15.03	18.4
134	0.97617	0.0	21.89	0	0.624	5.757	98.4	2.3460	4	437	21.2	17.31	15.6

The top 10 suburbs with ptration have a low rates far away below the max value of 88.97%.

(f)

# The value of chas is 1 1 if the suburb tracts bounds river
Boston['chas'].value_counts()[1]

35

There are 35 suburbs which bound the Charles river

(g)

Boston['ptratio'].median()

19.05

(h)

Boston['medv'].argmin()

398

Boston.loc[398]

crim        38.3518
zn           0.0000
indus       18.1000
chas         0.0000
nox          0.6930
rm           5.4530
age        100.0000
dis          1.4896
rad         24.0000
tax        666.0000
ptratio     20.2000
lstat       30.5900
medv         5.0000
Name: 398, dtype: float64

Boston.describe()

	crim	zn	indus	chas	nox	rm	age	dis	rad	tax	ptratio	lstat	medv
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
mean	3.613524	11.363636	11.136779	0.069170	0.554695	6.284634	68.574901	3.795043	9.549407	408.237154	18.455534	12.653063	22.532806
std	8.601545	23.322453	6.860353	0.253994	0.115878	0.702617	28.148861	2.105710	8.707259	168.537116	2.164946	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	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	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	11.360000	21.200000
75%	3.677083	12.500000	18.100000	0.000000	0.624000	6.623500	94.075000	5.188425	24.000000	666.000000	20.200000	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	37.970000	50.000000

The suburb no 398 has the lowest median value of owner occupied homes.
As far as this suburb is concerned, the other predictors are located in the following quantiles: - Above 75% quantile we find crim, indus, nox, age, rad, tax, ptratio and lstat. Particularly, age, rad and ptratio attend their max values; - Below 25% quantile we find zn, rm, dis and medv. Particularly, both medv and zn attend their min value.

(i)

#More than average of 7 rooms per dwelling
len(Boston[Boston['rm']>7])

64

#More than average of 8 rooms per dwelling
len(Boston[Boston['rm']>8])

13

Boston[Boston['rm']>8].describe()

	crim	zn	indus	chas	nox	rm	age	dis	rad	tax	ptratio	lstat	medv
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
mean	0.718795	13.615385	7.078462	0.153846	0.539238	8.348538	71.538462	3.430192	7.461538	325.076923	16.361538	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	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	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	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	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	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	7.440000	50.000000

There are 64 and 13 suburbs which have more than 7 and 8 rooms per dewilling respectively.
Furthermore, the average of crime rate for the 13 suburbs is lower than crime rate for the whole population. However, median value of owner-occupied homes is larger as expected.