Introduction

Author

Alfa Pradana

Load library

import pandas as pd
import numpy as np
pd.__version__
'2.2.3'

Data preparation

car = pd.read_csv('https://raw.githubusercontent.com/alexeygrigorev/datasets/master/car_fuel_efficiency.csv')
car.head()
engine_displacement num_cylinders horsepower vehicle_weight acceleration model_year origin fuel_type drivetrain num_doors fuel_efficiency_mpg
0 170 3.0 159.0 3413.433759 17.7 2003 Europe Gasoline All-wheel drive 0.0 13.231729
1 130 5.0 97.0 3149.664934 17.8 2007 USA Gasoline Front-wheel drive 0.0 13.688217
2 170 NaN 78.0 3079.038997 15.1 2018 Europe Gasoline Front-wheel drive 0.0 14.246341
3 220 4.0 NaN 2542.392402 20.2 2009 USA Diesel All-wheel drive 2.0 16.912736
4 210 1.0 140.0 3460.870990 14.4 2009 Europe Gasoline All-wheel drive 2.0 12.488369

Record count

car.shape[0]
9704

Fuel types

car.fuel_type.describe()
count         9704
unique           2
top       Gasoline
freq          4898
Name: fuel_type, dtype: object

The distribution of the target variable fuel_efficiency_mpg looks like the normal distribution so no need the log transformation.

Handling missing values

car.isnull().sum()
engine_displacement      0
num_cylinders          482
horsepower             708
vehicle_weight           0
acceleration           930
model_year               0
origin                   0
fuel_type                0
drivetrain               0
num_doors              502
fuel_efficiency_mpg      0
dtype: int64

Max fuel efficiency

car.groupby('origin').fuel_efficiency_mpg.max()
origin
Asia      23.759123
Europe    25.967222
USA       24.971452
Name: fuel_efficiency_mpg, dtype: float64

Median value of horsepower

car.horsepower
0       159.0
1        97.0
2        78.0
3         NaN
4       140.0
        ...  
9699    164.0
9700    154.0
9701    138.0
9702    177.0
9703    140.0
Name: horsepower, Length: 9704, dtype: float64
med_before = car.horsepower.median()
med_before
np.float64(149.0)
most_freq = car.horsepower.mode()[0]
most_freq
np.float64(152.0)
car.horsepower = car.horsepower.fillna(most_freq)
car.horsepower
0       159.0
1        97.0
2        78.0
3       152.0
4       140.0
        ...  
9699    164.0
9700    154.0
9701    138.0
9702    177.0
9703    140.0
Name: horsepower, Length: 9704, dtype: float64
med_after = car.horsepower.median()
med_after
np.float64(152.0)

Sum of weights

asian_car = car[car['origin'] == 'Asia']
asian_car
engine_displacement num_cylinders horsepower vehicle_weight acceleration model_year origin fuel_type drivetrain num_doors fuel_efficiency_mpg
8 250 1.0 174.0 2714.219310 10.3 2016 Asia Diesel Front-wheel drive -1.0 16.823554
12 320 5.0 145.0 2783.868974 15.1 2010 Asia Diesel All-wheel drive 1.0 16.175820
14 200 6.0 160.0 3582.687368 14.9 2007 Asia Diesel All-wheel drive 0.0 11.871091
20 150 3.0 197.0 2231.808142 18.7 2011 Asia Gasoline Front-wheel drive 1.0 18.889083
21 160 4.0 133.0 2659.431451 NaN 2016 Asia Gasoline Front-wheel drive -1.0 16.077730
... ... ... ... ... ... ... ... ... ... ... ...
9688 260 4.0 152.0 3948.404625 15.5 2018 Asia Diesel All-wheel drive -1.0 11.054830
9692 180 3.0 188.0 3680.341381 18.0 2016 Asia Gasoline Front-wheel drive 1.0 11.711653
9693 280 2.0 148.0 2545.070139 15.6 2012 Asia Diesel All-wheel drive 0.0 17.202782
9698 180 1.0 131.0 3107.427820 13.2 2005 Asia Gasoline Front-wheel drive -2.0 13.933716
9703 270 3.0 140.0 2908.043477 14.7 2005 Asia Diesel All-wheel drive -1.0 14.884467

3247 rows × 11 columns

sel_asian_car = asian_car[['vehicle_weight', 'model_year']].head(7)
sel_asian_car
vehicle_weight model_year
8 2714.219310 2016
12 2783.868974 2010
14 3582.687368 2007
20 2231.808142 2011
21 2659.431451 2016
34 2844.227534 2014
38 3761.994038 2019 
X = sel_asian_car.values
X
array([[2714.21930965, 2016.        ],
       [2783.86897424, 2010.        ],
       [3582.68736772, 2007.        ],
       [2231.8081416 , 2011.        ],
       [2659.43145076, 2016.        ],
       [2844.22753389, 2014.        ],
       [3761.99403819, 2019.        ]])
XTX = X.T.dot(X)
XTX_inv = np.linalg.inv(XTX)
y = np.array([1100, 1300, 800, 900, 1000, 1100, 1200])
w = XTX_inv.dot(X.T).dot(y)
w.sum()
np.float64(0.5187709081074016)