In [13]:

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

import statsmodels.formula.api as smf
import statsmodels.api as sm

In [2]:

# Function to print all information about DataFrame
def review_dataframe(df):
    print(" DATA INFO ".center(125,'-'))
    print(df.info())
    
    print(" SHAPE OF DATASET ".center(125,'-'))
    print('Rows:{}'.format(df.shape[0]))
    print('Columns:{}'.format(df.shape[1]))
    
    print(" DATA TYPES ".center(125,'-'))
    print(df.dtypes)
    
    print(" STATISTICS OF DATA ".center(125,'-'))
    print(df.describe(include="all"))
    
    print(" MISSING VALUES ".center(125,'-'))
    print(df.isnull().sum()[df.isnull().sum()>0].sort_values(ascending = False))
    
    print(" DUPLICATED VALUES ".center(125,'-'))
    print(df.duplicated().sum())

In [3]:

df_cars = pd.read_csv('data/cars.csv')
df_cars.head()

Out[3]:

	car_ID	symboling	CarName	fueltype	aspiration	doornumber	carbody	drivewheel	enginelocation	wheelbase	...	enginesize	fuelsystem	boreratio	stroke	compressionratio	horsepower	peakrpm	citympg	highwaympg	price
0	1	3	alfa-romero giulia	gas	std	two	convertible	rwd	front	88.6	...	130	mpfi	3.47	2.68	9.0	111	5000	21	27	13495.0
1	2	3	alfa-romero stelvio	gas	std	two	convertible	rwd	front	88.6	...	130	mpfi	3.47	2.68	9.0	111	5000	21	27	16500.0
2	3	1	alfa-romero Quadrifoglio	gas	std	two	hatchback	rwd	front	94.5	...	152	mpfi	2.68	3.47	9.0	154	5000	19	26	16500.0
3	4	2	audi 100 ls	gas	std	four	sedan	fwd	front	99.8	...	109	mpfi	3.19	3.40	10.0	102	5500	24	30	13950.0
4	5	2	audi 100ls	gas	std	four	sedan	4wd	front	99.4	...	136	mpfi	3.19	3.40	8.0	115	5500	18	22	17450.0

5 rows × 26 columns

In [4]:

review_dataframe(df_cars)

--------------------------------------------------------- DATA INFO ---------------------------------------------------------
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 205 entries, 0 to 204
Data columns (total 26 columns):
 #   Column            Non-Null Count  Dtype  
---  ------            --------------  -----  
 0   car_ID            205 non-null    int64  
 1   symboling         205 non-null    int64  
 2   CarName           205 non-null    object 
 3   fueltype          205 non-null    object 
 4   aspiration        205 non-null    object 
 5   doornumber        205 non-null    object 
 6   carbody           205 non-null    object 
 7   drivewheel        205 non-null    object 
 8   enginelocation    205 non-null    object 
 9   wheelbase         205 non-null    float64
 10  carlength         205 non-null    float64
 11  carwidth          205 non-null    float64
 12  carheight         205 non-null    float64
 13  curbweight        205 non-null    int64  
 14  enginetype        205 non-null    object 
 15  cylindernumber    205 non-null    object 
 16  enginesize        205 non-null    int64  
 17  fuelsystem        205 non-null    object 
 18  boreratio         205 non-null    float64
 19  stroke            205 non-null    float64
 20  compressionratio  205 non-null    float64
 21  horsepower        205 non-null    int64  
 22  peakrpm           205 non-null    int64  
 23  citympg           205 non-null    int64  
 24  highwaympg        205 non-null    int64  
 25  price             205 non-null    float64
dtypes: float64(8), int64(8), object(10)
memory usage: 41.8+ KB
None
------------------------------------------------------ SHAPE OF DATASET -----------------------------------------------------
Rows:205
Columns:26
--------------------------------------------------------- DATA TYPES --------------------------------------------------------
car_ID                int64
symboling             int64
CarName              object
fueltype             object
aspiration           object
doornumber           object
carbody              object
drivewheel           object
enginelocation       object
wheelbase           float64
carlength           float64
carwidth            float64
carheight           float64
curbweight            int64
enginetype           object
cylindernumber       object
enginesize            int64
fuelsystem           object
boreratio           float64
stroke              float64
compressionratio    float64
horsepower            int64
peakrpm               int64
citympg               int64
highwaympg            int64
price               float64
dtype: object
----------------------------------------------------- STATISTICS OF DATA ----------------------------------------------------
            car_ID   symboling        CarName fueltype aspiration doornumber  \
count   205.000000  205.000000            205      205        205        205   
unique         NaN         NaN            147        2          2          2   
top            NaN         NaN  toyota corona      gas        std       four   
freq           NaN         NaN              6      185        168        115   
mean    103.000000    0.834146            NaN      NaN        NaN        NaN   
std      59.322565    1.245307            NaN      NaN        NaN        NaN   
min       1.000000   -2.000000            NaN      NaN        NaN        NaN   
25%      52.000000    0.000000            NaN      NaN        NaN        NaN   
50%     103.000000    1.000000            NaN      NaN        NaN        NaN   
75%     154.000000    2.000000            NaN      NaN        NaN        NaN   
max     205.000000    3.000000            NaN      NaN        NaN        NaN   

       carbody drivewheel enginelocation   wheelbase  ...  enginesize  \
count      205        205            205  205.000000  ...  205.000000   
unique       5          3              2         NaN  ...         NaN   
top      sedan        fwd          front         NaN  ...         NaN   
freq        96        120            202         NaN  ...         NaN   
mean       NaN        NaN            NaN   98.756585  ...  126.907317   
std        NaN        NaN            NaN    6.021776  ...   41.642693   
min        NaN        NaN            NaN   86.600000  ...   61.000000   
25%        NaN        NaN            NaN   94.500000  ...   97.000000   
50%        NaN        NaN            NaN   97.000000  ...  120.000000   
75%        NaN        NaN            NaN  102.400000  ...  141.000000   
max        NaN        NaN            NaN  120.900000  ...  326.000000   

        fuelsystem   boreratio      stroke compressionratio  horsepower  \
count          205  205.000000  205.000000       205.000000  205.000000   
unique           8         NaN         NaN              NaN         NaN   
top           mpfi         NaN         NaN              NaN         NaN   
freq            94         NaN         NaN              NaN         NaN   
mean           NaN    3.329756    3.255415        10.142537  104.117073   
std            NaN    0.270844    0.313597         3.972040   39.544167   
min            NaN    2.540000    2.070000         7.000000   48.000000   
25%            NaN    3.150000    3.110000         8.600000   70.000000   
50%            NaN    3.310000    3.290000         9.000000   95.000000   
75%            NaN    3.580000    3.410000         9.400000  116.000000   
max            NaN    3.940000    4.170000        23.000000  288.000000   

            peakrpm     citympg  highwaympg         price  
count    205.000000  205.000000  205.000000    205.000000  
unique          NaN         NaN         NaN           NaN  
top             NaN         NaN         NaN           NaN  
freq            NaN         NaN         NaN           NaN  
mean    5125.121951   25.219512   30.751220  13276.710571  
std      476.985643    6.542142    6.886443   7988.852332  
min     4150.000000   13.000000   16.000000   5118.000000  
25%     4800.000000   19.000000   25.000000   7788.000000  
50%     5200.000000   24.000000   30.000000  10295.000000  
75%     5500.000000   30.000000   34.000000  16503.000000  
max     6600.000000   49.000000   54.000000  45400.000000  

[11 rows x 26 columns]
------------------------------------------------------- MISSING VALUES ------------------------------------------------------
Series([], dtype: int64)
----------------------------------------------------- DUPLICATED VALUES -----------------------------------------------------
0

In [5]:

# Add auto mark (company)
df_cars['company'] = df_cars['CarName'].apply(lambda x : x.split(' ')[0])
print(f'Number of cars companies: {df_cars.company.nunique()}')
print(df_cars.company.unique())

Number of cars companies: 28
['alfa-romero' 'audi' 'bmw' 'chevrolet' 'dodge' 'honda' 'isuzu' 'jaguar'
 'maxda' 'mazda' 'buick' 'mercury' 'mitsubishi' 'Nissan' 'nissan'
 'peugeot' 'plymouth' 'porsche' 'porcshce' 'renault' 'saab' 'subaru'
 'toyota' 'toyouta' 'vokswagen' 'volkswagen' 'vw' 'volvo']

In [6]:

def fix_company_name(old_name, new_name):
    df_cars.company.replace(old_name, new_name, inplace=True)

In [7]:

# to lower register (for example 'Nissan' and 'nissan')
df_cars.company = df_cars.company.str.capitalize()

# Change for right versions
fix_company_name('Alfa-romero', 'Alfa-Romero')
fix_company_name('Bmw', 'BMW')
fix_company_name('Maxda', 'Mazda')
fix_company_name('Porcshce', 'Porsche')
fix_company_name('Toyouta', 'Toyota')
fix_company_name('Vokswagen', 'Volkswagen')
fix_company_name('Vw', 'Volkswagen')

print(f'Number of cars companies: {df_cars.company.nunique()}')
print(df_cars.company.unique())

Number of cars companies: 22
['Alfa-Romero' 'Audi' 'BMW' 'Chevrolet' 'Dodge' 'Honda' 'Isuzu' 'Jaguar'
 'Mazda' 'Buick' 'Mercury' 'Mitsubishi' 'Nissan' 'Peugeot' 'Plymouth'
 'Porsche' 'Renault' 'Saab' 'Subaru' 'Toyota' 'Volkswagen' 'Volvo']

In [8]:

# Use this predictors, filter df
nec_columns = ['company', 'fueltype', 'aspiration', 'carbody', 'drivewheel', 'wheelbase', 
               'carlength', 'carwidth', 'curbweight', 'enginetype', 'cylindernumber', 
               'enginesize', 'boreratio', 'horsepower', 'price'
              ]
df_cars_filt = df_cars[nec_columns]
df_cars_filt

Out[8]:

	company	fueltype	aspiration	carbody	drivewheel	wheelbase	carlength	carwidth	curbweight	enginetype	cylindernumber	enginesize	boreratio	horsepower	price
0	Alfa-Romero	gas	std	convertible	rwd	88.6	168.8	64.1	2548	dohc	four	130	3.47	111	13495.0
1	Alfa-Romero	gas	std	convertible	rwd	88.6	168.8	64.1	2548	dohc	four	130	3.47	111	16500.0
2	Alfa-Romero	gas	std	hatchback	rwd	94.5	171.2	65.5	2823	ohcv	six	152	2.68	154	16500.0
3	Audi	gas	std	sedan	fwd	99.8	176.6	66.2	2337	ohc	four	109	3.19	102	13950.0
4	Audi	gas	std	sedan	4wd	99.4	176.6	66.4	2824	ohc	five	136	3.19	115	17450.0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
200	Volvo	gas	std	sedan	rwd	109.1	188.8	68.9	2952	ohc	four	141	3.78	114	16845.0
201	Volvo	gas	turbo	sedan	rwd	109.1	188.8	68.8	3049	ohc	four	141	3.78	160	19045.0
202	Volvo	gas	std	sedan	rwd	109.1	188.8	68.9	3012	ohcv	six	173	3.58	134	21485.0
203	Volvo	diesel	turbo	sedan	rwd	109.1	188.8	68.9	3217	ohc	six	145	3.01	106	22470.0
204	Volvo	gas	turbo	sedan	rwd	109.1	188.8	68.9	3062	ohc	four	141	3.78	114	22625.0

205 rows × 15 columns

In [9]:

plt.figure(figsize=(11, 9))
sns.heatmap(df_cars_filt.corr(), annot=True, cmap='coolwarm', fmt='.3f')
plt.title('Correlation matrix')
plt.show()

C:\Users\gpapu\AppData\Local\Temp\ipykernel_18372\158818267.py:2: 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.
  sns.heatmap(df_cars_filt.corr(), annot=True, cmap='coolwarm', fmt='.3f')

In [12]:

# for using linear regression change object type
df_dummy = pd.get_dummies(data=df_cars_filt[['company', 'fueltype', 'aspiration', 'carbody', 
                                             'drivewheel', 'enginetype', 'cylindernumber']], 
                          drop_first=True)
df_cars_LR = pd.concat([df_cars_filt.drop(['company', 'fueltype', 'aspiration', 'carbody', 
                                           'drivewheel', 'enginetype', 'cylindernumber'],
                                          axis='columns'), 
                        df_dummy], axis=1)
df_cars_LR

Out[12]:

	wheelbase	carlength	carwidth	curbweight	enginesize	boreratio	horsepower	price	company_Audi	company_BMW	...	enginetype_ohc	enginetype_ohcf	enginetype_ohcv	enginetype_rotor	cylindernumber_five	cylindernumber_four	cylindernumber_six	cylindernumber_three	cylindernumber_twelve	cylindernumber_two
0	88.6	168.8	64.1	2548	130	3.47	111	13495.0	0	0	...	0	0	0	0	0	1	0	0	0	0
1	88.6	168.8	64.1	2548	130	3.47	111	16500.0	0	0	...	0	0	0	0	0	1	0	0	0	0
2	94.5	171.2	65.5	2823	152	2.68	154	16500.0	0	0	...	0	0	1	0	0	0	1	0	0	0
3	99.8	176.6	66.2	2337	109	3.19	102	13950.0	1	0	...	1	0	0	0	0	1	0	0	0	0
4	99.4	176.6	66.4	2824	136	3.19	115	17450.0	1	0	...	1	0	0	0	1	0	0	0	0	0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
200	109.1	188.8	68.9	2952	141	3.78	114	16845.0	0	0	...	1	0	0	0	0	1	0	0	0	0
201	109.1	188.8	68.8	3049	141	3.78	160	19045.0	0	0	...	1	0	0	0	0	1	0	0	0	0
202	109.1	188.8	68.9	3012	173	3.58	134	21485.0	0	0	...	0	0	1	0	0	0	1	0	0	0
203	109.1	188.8	68.9	3217	145	3.01	106	22470.0	0	0	...	1	0	0	0	0	0	1	0	0	0
204	109.1	188.8	68.9	3062	141	3.78	114	22625.0	0	0	...	1	0	0	0	0	1	0	0	0	0

205 rows × 49 columns

In [15]:

# model with one price predictor - horsepower
result = smf.ols('price ~ horsepower', df_cars_LR).fit()
result.summary()

Out[15]:

OLS Regression Results
Dep. Variable:	price	R-squared:	0.653
Model:	OLS	Adj. R-squared:	0.651
Method:	Least Squares	F-statistic:	382.2
Date:	Fri, 18 Aug 2023	Prob (F-statistic):	1.48e-48
Time:	20:52:31	Log-Likelihood:	-2024.0
No. Observations:	205	AIC:	4052.
Df Residuals:	203	BIC:	4059.
Df Model:	1
Covariance Type:	nonrobust

	coef	std err	t	P>\|t\|	[0.025	0.975]
Intercept	-3721.7615	929.849	-4.003	0.000	-5555.163	-1888.360
horsepower	163.2631	8.351	19.549	0.000	146.796	179.730

Omnibus:	47.741	Durbin-Watson:	0.792
Prob(Omnibus):	0.000	Jarque-Bera (JB):	91.702
Skew:	1.141	Prob(JB):	1.22e-20
Kurtosis:	5.352	Cond. No.	314.

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

In [18]:

# Make 2 models:
#     - with all predictors
#     - with all predictors except for car brands
X = df_cars_LR.drop(['price'], axis='columns')
X = sm.add_constant(X)
Y = df_cars_LR['price']

model_1 = sm.OLS(Y, X).fit()
model_1.summary()

Out[18]:

OLS Regression Results
Dep. Variable:	price	R-squared:	0.959
Model:	OLS	Adj. R-squared:	0.948
Method:	Least Squares	F-statistic:	81.09
Date:	Fri, 18 Aug 2023	Prob (F-statistic):	4.86e-89
Time:	20:58:54	Log-Likelihood:	-1804.2
No. Observations:	205	AIC:	3702.
Df Residuals:	158	BIC:	3858.
Df Model:	46
Covariance Type:	nonrobust

	coef	std err	t	P>\|t\|	[0.025	0.975]
const	-3.472e+04	1.17e+04	-2.959	0.004	-5.79e+04	-1.15e+04
wheelbase	147.1396	76.234	1.930	0.055	-3.429	297.708
carlength	-113.2012	48.949	-2.313	0.022	-209.881	-16.522
carwidth	809.1860	214.508	3.772	0.000	385.514	1232.858
curbweight	4.1822	1.582	2.643	0.009	1.057	7.307
enginesize	61.4212	23.643	2.598	0.010	14.724	108.119
boreratio	-4319.4728	1759.825	-2.454	0.015	-7795.288	-843.657
horsepower	34.7010	18.000	1.928	0.056	-0.850	70.252
company_Audi	437.1040	2125.971	0.206	0.837	-3761.885	4636.093
company_BMW	7993.4998	2105.132	3.797	0.000	3835.671	1.22e+04
company_Buick	3431.0969	2472.252	1.388	0.167	-1451.829	8314.023
company_Chevrolet	-2107.0167	2054.269	-1.026	0.307	-6164.387	1950.353
company_Dodge	-3034.5530	1686.337	-1.799	0.074	-6365.224	296.118
company_Honda	-2328.7396	1622.141	-1.436	0.153	-5532.617	875.138
company_Isuzu	-926.1643	1819.489	-0.509	0.611	-4519.823	2667.495
company_Jaguar	2695.2664	2546.268	1.059	0.291	-2333.847	7724.379
company_Mazda	-1291.5657	1652.561	-0.782	0.436	-4555.527	1972.395
company_Mercury	-2762.0259	2786.701	-0.991	0.323	-8266.016	2741.965
company_Mitsubishi	-3699.6473	1650.046	-2.242	0.026	-6958.640	-440.654
company_Nissan	-1488.1217	1563.564	-0.952	0.343	-4576.305	1600.061
company_Peugeot	-2671.4595	1795.328	-1.488	0.139	-6217.398	874.479
company_Plymouth	-3052.1258	1670.829	-1.827	0.070	-6352.166	247.915
company_Porsche	4915.9715	2797.761	1.757	0.081	-609.864	1.04e+04
company_Renault	-2865.2197	2073.046	-1.382	0.169	-6959.676	1229.237
company_Saab	719.8222	1767.620	0.407	0.684	-2771.390	4211.035
company_Subaru	-1.164e+04	3416.221	-3.407	0.001	-1.84e+04	-4892.375
company_Toyota	-2608.7871	1539.320	-1.695	0.092	-5649.086	431.512
company_Volkswagen	-2261.9355	1606.886	-1.408	0.161	-5435.683	911.812
company_Volvo	68.2605	1943.170	0.035	0.972	-3769.679	3906.200
fueltype_gas	-243.7792	908.310	-0.268	0.789	-2037.774	1550.216
aspiration_turbo	596.6566	676.548	0.882	0.379	-739.588	1932.902
carbody_hardtop	-2556.7157	1213.929	-2.106	0.037	-4954.337	-159.094
carbody_hatchback	-3044.4196	1107.064	-2.750	0.007	-5230.972	-857.867
carbody_sedan	-2256.9173	1154.971	-1.954	0.052	-4538.090	24.256
carbody_wagon	-2815.4970	1223.156	-2.302	0.023	-5231.343	-399.651
drivewheel_fwd	-169.4926	888.585	-0.191	0.849	-1924.531	1585.545
drivewheel_rwd	231.9066	1039.685	0.223	0.824	-1821.566	2285.380
enginetype_dohcv	-8358.0756	4326.239	-1.932	0.055	-1.69e+04	186.645
enginetype_l	-1067.3120	1602.125	-0.666	0.506	-4231.657	2097.033
enginetype_ohc	-273.7175	1063.557	-0.257	0.797	-2374.341	1826.906
enginetype_ohcf	1.031e+04	2672.508	3.857	0.000	5028.873	1.56e+04
enginetype_ohcv	-2393.8587	1214.631	-1.971	0.050	-4792.867	5.150
enginetype_rotor	37.4715	2092.597	0.018	0.986	-4095.600	4170.543
cylindernumber_five	-5235.5232	2887.214	-1.813	0.072	-1.09e+04	466.990
cylindernumber_four	-3741.3604	3542.130	-1.056	0.292	-1.07e+04	3254.673
cylindernumber_six	-5441.5317	2628.646	-2.070	0.040	-1.06e+04	-249.713
cylindernumber_three	1604.1476	2774.698	0.578	0.564	-3876.137	7084.432
cylindernumber_twelve	-8097.1585	3616.336	-2.239	0.027	-1.52e+04	-954.561
cylindernumber_two	37.4715	2092.597	0.018	0.986	-4095.600	4170.543

Omnibus:	81.075	Durbin-Watson:	1.382
Prob(Omnibus):	0.000	Jarque-Bera (JB):	487.187
Skew:	1.379	Prob(JB):	1.62e-106
Kurtosis:	10.031	Cond. No.	1.02e+16

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The smallest eigenvalue is 1.35e-23. This might indicate that there are
strong multicollinearity problems or that the design matrix is singular.

In [23]:

columns_to_keep = df_cars_LR.columns[~df_cars_LR.columns.str.startswith('company_')]
X = df_cars_LR[columns_to_keep].drop('price', axis='columns')
X = sm.add_constant(X)
Y = df_cars_LR.price
model_2 = sm.OLS(Y, X).fit()
model_2.summary()

Out[23]:

OLS Regression Results
Dep. Variable:	price	R-squared:	0.914
Model:	OLS	Adj. R-squared:	0.901
Method:	Least Squares	F-statistic:	72.32
Date:	Fri, 18 Aug 2023	Prob (F-statistic):	9.86e-81
Time:	21:12:34	Log-Likelihood:	-1881.6
No. Observations:	205	AIC:	3817.
Df Residuals:	178	BIC:	3907.
Df Model:	26
Covariance Type:	nonrobust

	coef	std err	t	P>\|t\|	[0.025	0.975]
const	-1.7e+04	1.3e+04	-1.309	0.192	-4.26e+04	8625.219
wheelbase	71.1868	87.028	0.818	0.414	-100.552	242.925
carlength	-51.3497	50.341	-1.020	0.309	-150.692	47.993
carwidth	541.8700	253.327	2.139	0.034	41.958	1041.782
curbweight	2.9577	1.796	1.647	0.101	-0.585	6.501
enginesize	36.0515	22.376	1.611	0.109	-8.105	80.208
boreratio	-2230.4519	1731.681	-1.288	0.199	-5647.719	1186.815
horsepower	86.8164	16.717	5.193	0.000	53.827	119.806
fueltype_gas	-2423.0935	975.579	-2.484	0.014	-4348.283	-497.904
aspiration_turbo	-1139.2334	787.230	-1.447	0.150	-2692.738	414.271
carbody_hardtop	-3728.0949	1519.366	-2.454	0.015	-6726.383	-729.807
carbody_hatchback	-4639.1279	1294.594	-3.583	0.000	-7193.855	-2084.401
carbody_sedan	-3337.7854	1356.075	-2.461	0.015	-6013.838	-661.732
carbody_wagon	-4315.4661	1465.089	-2.946	0.004	-7206.646	-1424.287
drivewheel_fwd	297.2402	1121.766	0.265	0.791	-1916.431	2510.912
drivewheel_rwd	1939.1594	1226.536	1.581	0.116	-481.263	4359.582
enginetype_dohcv	-1.713e+04	4540.120	-3.773	0.000	-2.61e+04	-8171.142
enginetype_l	2176.0521	1332.818	1.633	0.104	-454.106	4806.211
enginetype_ohc	4006.5687	897.437	4.464	0.000	2235.584	5777.553
enginetype_ohcf	5421.2822	1388.078	3.906	0.000	2682.076	8160.488
enginetype_ohcv	-5001.2242	1345.435	-3.717	0.000	-7656.280	-2346.169
enginetype_rotor	-5196.6413	2084.532	-2.493	0.014	-9310.217	-1083.066
cylindernumber_five	-1.389e+04	2891.599	-4.802	0.000	-1.96e+04	-8180.353
cylindernumber_four	-1.618e+04	3243.610	-4.989	0.000	-2.26e+04	-9780.800
cylindernumber_six	-1.175e+04	2287.516	-5.135	0.000	-1.63e+04	-7231.547
cylindernumber_three	-9264.0553	4750.899	-1.950	0.053	-1.86e+04	111.279
cylindernumber_twelve	-1.214e+04	3386.507	-3.585	0.000	-1.88e+04	-5458.378
cylindernumber_two	-5196.6413	2084.532	-2.493	0.014	-9310.217	-1083.066

Omnibus:	18.493	Durbin-Watson:	1.249
Prob(Omnibus):	0.000	Jarque-Bera (JB):	50.728
Skew:	0.293	Prob(JB):	9.65e-12
Kurtosis:	5.365	Cond. No.	1.02e+16

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The smallest eigenvalue is 1.35e-23. This might indicate that there are
strong multicollinearity problems or that the design matrix is singular.

It is better to choose the model with the least number of predictors, since R2 has not changed very much, and some brands are not significant at all¶

The chosen model explains 90% of the variance. Among the predictors (10 out of 27) were insignificant (p > 0.05). With a single change in the horsepower indicator, the price increases by 86.8164¶