
import numpy as np
import pandas as pd
import os
import matplotlib.pyplot as plt
pd.options.mode.chained_assignment = None  # removes warning messages



os.chdir("C:\\Users\\ASUS")
insurance = pd.read_csv("insurance.csv")

# Preview our data
insurance.head()


# Showing the properties of different variables
insurance.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 1338 entries, 0 to 1337
Data columns (total 7 columns):
 #   Column    Non-Null Count  Dtype  
---  ------    --------------  -----  
 0   age       1338 non-null   int64  
 1   sex       1338 non-null   object 
 2   bmi       1338 non-null   float64
 3   children  1338 non-null   int64  
 4   smoker    1338 non-null   object 
 5   region    1338 non-null   object 
 6   charges   1338 non-null   float64
dtypes: float64(2), int64(2), object(3)
memory usage: 73.3+ KB


insurance.isnull().sum()

age         0
sex         0
bmi         0
children    0
smoker      0
region      0
charges     0
dtype: int64


insurance.corr()


fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(12, 10))
insurance.plot(kind="hist", y="age", bins=70, color="b", ax=axes[0][0])
insurance.plot(kind="hist", y="bmi", bins=100, color="r", ax=axes[0][1])
insurance.plot(kind="hist", y="children", bins=6, color="g", ax=axes[1][0])
insurance.plot(kind="hist", y="charges", bins=100, color="orange", ax=axes[1][1])
plt.show()


import seaborn as sns  # Imorting Seaborn library
#pal = ["#FA5858", "#58D3F7"]
sns.scatterplot(x="bmi", y="charges", data=insurance, palette=pal, hue='smoker')

<AxesSubplot:xlabel='bmi', ylabel='charges'>


import seaborn as sns

sns.set(style="ticks")
pal = ["#FA5858", "#58D3F7"]

sns.pairplot(insurance, hue="smoker", palette=pal)
plt.title("Smokers")

Text(0.5, 1.0, 'Smokers')


insurance.head()


insurance=pd.get_dummies(data=insurance,columns=['sex', 'smoker',"region"],drop_first=True)


insurance.head(3)


#segregate data into dependent and independent variables

X = insurance.drop("charges", axis = 1)#independent variables
y = insurance["charges"]#dependent variable


# Splitting it into training and testing (70% train & 30% test)
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.3, random_state = 42)


# Concatenating the training data to create a single dataset
df = pd.concat([y_train,X_train],axis=1)
df.head()


import statsmodels.formula.api as sm
rock=sm.ols(formula=
"""charges ~ age+ bmi + children + sex_male + smoker_yes + 
region_northwest + region_southeast + region_southwest""",
data=df).fit()
rock.summary()# shows total summary


# Remove first sex_male followed by region_northwest
import statsmodels.formula.api as sm
rock=sm.ols(formula=
"""charges ~ age+ bmi + children  + smoker_yes + 
 region_southeast + region_southwest""",
data=insurance).fit()
rock.summary()# shows total summary


var = pd.DataFrame(round(rock.pvalues,3))# shows p value
#var["coeff"] = rock.params#coefficients
from statsmodels.stats.outliers_influence import variance_inflation_factor
variables = rock.model.exog #.if I had saved data as rock
# this it would have looked like rock.model.exog
vif = [variance_inflation_factor(variables, i) for i in range(variables.shape[1])]
vif 
var["vif"] = vif
var


# Creating a single dataset with the testing data
df1 = pd.concat([y_test,X_test],axis=1)
#predict the test data with the model
df1["pred"] = rock.predict(X_test)
df1.head()


from sklearn.metrics import mean_absolute_percentage_error
mean_absolute_percentage_error(df1["charges"],df1["pred"])*100

42.1614163772496


# Feature Scaling
from sklearn.preprocessing import StandardScaler
sc = StandardScaler()
X_train = sc.fit_transform(X_train)
X_test = sc.transform(X_test)


from sklearn.svm import SVR
svr = SVR(kernel = 'rbf')
svr.fit(X_train, y_train)

SVR()


# Predict the model
y_pred = svr.predict(X_test)


from sklearn.metrics import mean_absolute_percentage_error
mean_absolute_percentage_error(y_test,y_pred)*100

103.25108812337018


d = pd.DataFrame()
d["test_y"] = y_test
d["y_pred"] = y_pred

#Mape with formula
d["mp"] = abs((d["test_y"]- d["y_pred"])/d["test_y"])
(d.mp.mean())*100#mape

103.25108812337018


parameters={"kernel":['linear', 'poly', 'rbf', 'sigmoid'],
'gamma': ['scale', 'auto'] }


from sklearn.model_selection import GridSearchCV
grid_search = GridSearchCV(estimator = svr,
param_grid = parameters, n_jobs = -1)#n_jobs = -1 will apply all CPUs

grid_search.fit(X_train, y_train)

y_pred = grid_search.predict(X_test)


grid_search.best_params_

{'gamma': 'scale', 'kernel': 'linear'}


from sklearn.metrics import mean_absolute_percentage_error
mean_absolute_percentage_error(y_test,y_pred)*100

92.1504136167104


from sklearn.ensemble import RandomForestRegressor
rf = RandomForestRegressor(n_estimators = 1000, random_state = 42)
rf.fit(X_train, y_train)

RandomForestRegressor(n_estimators=1000, random_state=42)


# Predict the model
y_pred = rf.predict(X_test)


from sklearn.metrics import mean_absolute_percentage_error
mean_absolute_percentage_error(y_test,y_pred)*100

33.09156255231602


d = pd.DataFrame()
d["test_y"] = y_test
d["y_pred"] = y_pred

#Mape with formula
d["mp"] = abs((d["test_y"]- d["y_pred"])/d["test_y"])
(d.mp.mean())*100#mape

33.09156255231602


#Set the parameters
parameters={"max_depth":[5,10,15],
'min_samples_leaf': [3, 4, 5] }


#Set the grid search
from sklearn.model_selection import GridSearchCV
grid_search = GridSearchCV(estimator = rf,
param_grid = parameters, n_jobs = -1)#n_jobs = -1 will apply all CPUs


# Execute the grid search
grid_search.fit(X_train, y_train)

GridSearchCV(estimator=RandomForestRegressor(n_estimators=1000,
                                             random_state=42),
             n_jobs=-1,
             param_grid={'max_depth': [5, 10, 15],
                         'min_samples_leaf': [3, 4, 5]})


y_pred = grid_search.predict(X_test)
from sklearn.metrics import mean_absolute_percentage_error
mean_absolute_percentage_error(y_test,y_pred)*100

29.846981277483508

	age	bmi	children	charges
age	1.000000	0.109272	0.042469	0.299008
bmi	0.109272	1.000000	0.012759	0.198341
children	0.042469	0.012759	1.000000	0.067998
charges	0.299008	0.198341	0.067998	1.000000

	charges	age	bmi	children	sex_male	smoker_yes	region_northwest	region_southeast	region_southwest
332	13429.03540	61	31.160	0	0	0	1	0	0
355	24603.04837	46	27.600	0	1	0	0	0	1
138	27322.73386	54	31.900	3	0	0	0	1	0
381	42303.69215	55	30.685	0	1	1	0	0	0
292	42112.23560	25	45.540	2	1	1	0	1	0

Dep. Variable:	charges	R-squared:	0.742
Model:	OLS	Adj. R-squared:	0.740
Method:	Least Squares	F-statistic:	333.9
Date:	Wed, 22 Jun 2022	Prob (F-statistic):	6.51e-267
Time:	21:11:58	Log-Likelihood:	-9492.8
No. Observations:	936	AIC:	1.900e+04
Df Residuals:	927	BIC:	1.905e+04
Df Model:	8
Covariance Type:	nonrobust

	coef	std err	t	P>\|t\|	[0.025	0.975]
Intercept	-1.237e+04	1210.540	-10.222	0.000	-1.47e+04	-9998.247
age	261.2969	14.435	18.102	0.000	232.968	289.626
bmi	348.9069	35.285	9.888	0.000	279.659	418.154
children	424.1191	166.972	2.540	0.011	96.432	751.806
sex_male	104.8118	404.887	0.259	0.796	-689.790	899.413
smoker_yes	2.363e+04	498.610	47.388	0.000	2.26e+04	2.46e+04
region_northwest	-486.9346	570.048	-0.854	0.393	-1605.668	631.799
region_southeast	-970.9688	579.867	-1.674	0.094	-2108.973	167.036
region_southwest	-926.3229	578.431	-1.601	0.110	-2061.509	208.863

Omnibus:	224.792	Durbin-Watson:	2.075
Prob(Omnibus):	0.000	Jarque-Bera (JB):	543.466
Skew:	1.270	Prob(JB):	9.73e-119
Kurtosis:	5.735	Cond. No.	311.

	age	sex	bmi	children	smoker	region	charges
0	19	female	27.900	0	yes	southwest	16884.92400
1	18	male	33.770	1	no	southeast	1725.55230
2	28	male	33.000	3	no	southeast	4449.46200
3	33	male	22.705	0	no	northwest	21984.47061
4	32	male	28.880	0	no	northwest	3866.85520

	age	bmi	children	charges	sex_male	smoker_yes	region_southeast	region_southwest
0	19	27.90	0	16884.9240	0	1	0	1
1	18	33.77	1	1725.5523	1	0	1	0
2	28	33.00	3	4449.4620	1	0	1	0

Omnibus:	300.125	Durbin-Watson:	2.092
Prob(Omnibus):	0.000	Jarque-Bera (JB):	716.587
Skew:	1.211	Prob(JB):	2.48e-156
Kurtosis:	5.643	Cond. No.	295.

	0	vif
Intercept	0.000	32.859280
age	0.000	1.016174
bmi	0.000	1.104196
children	0.001	1.002831
smoker_yes	0.000	1.005747
region_southeast	0.039	1.244250
region_southwest	0.059	1.147367

	charges	age	bmi	children	sex_male	smoker_yes	region_northwest	pred
764	9095.06825	45	25.175	2	0	0	0	8868.289033
887	5272.17580	36	30.020	0	0	0	1	7252.860495
890	29330.98315	64	26.885	0	0	1	1	37231.273781
1293	9301.89355	46	25.745	3	1	0	1	9789.865128
259	33750.29180	19	31.920	0	1	1	1	27371.045323

	coef	std err	t	P>\|t\|	[0.025	0.975]
Intercept	-1.217e+04	949.538	-12.812	0.000	-1.4e+04	-1.03e+04
age	257.0064	11.889	21.617	0.000	233.683	280.330
bmi	338.6413	28.554	11.860	0.000	282.625	394.657
children	471.5441	137.656	3.426	0.001	201.498	741.590
smoker_yes	2.384e+04	411.659	57.921	0.000	2.3e+04	2.47e+04
region_southeast	-858.4696	415.206	-2.068	0.039	-1672.998	-43.941
region_southwest	-782.7452	413.756	-1.892	0.059	-1594.430	28.940

Purpose¶

Predicting Insurance Premiums¶

Aim¶

Machine Learning Algorithms used in the case study¶

We are going to import the data into Python¶

Observations: Here charges are our dependent variable, and we are going to predict it using the features (independent variables) like age, sex, bmi etc.¶

We can see that there are some categorical variables like sex, smoker, region; hence we are going to create dummy variables for them.¶

Missing values¶

Observations: we don't have any missing values in the data¶

Correlation¶

Observations: we don't have any alarming correlation among the independent variables. We will check it once again using vif, though.¶

Univariate analysis¶

Observations: We can see that all these variables are having variations. BMI seems to be almost a normally distributed.¶

Bivariate analysis¶

Observations: It's pretty clear that smokers are paying a higher premium than non-smokers. BMI doesn't seem to impacting the charges much.¶

Bivariate analysis - Pair plot¶

We are creating a pair plot and showing the impacts of smoker and non smokers on different variables¶

Preparing Data for Machine Learning Algorithms¶

Dummy Variable creation¶

We can see that we have few categorical variables like sex, smoker, region. Hence we need to create dummy variables for them.¶

All the dummy variables have been properly created¶

Data split¶

Segregating the independent variables as X and dependent variable as y¶

Now we will split the data into training (80% of the data) and rest 30% - named test, will be kept aside for later use.¶

We are concatenating the train and test so that we can easily use it for Linear regression. Later, we will use it (without concatenating) for SVM and Random Forest algorithms.¶

Modeling our Data¶

Linear Regression with stats model package¶

Remove insignificant variables (p value more than 0.05) and lowest absolute t value; one variable at a time.¶

Anova (Prob (F-statistic)) is less than 0.05, which ideally should be the case¶

p value of region_southwest (0.059) is slightly more than 0.05, but we can safely ignore it and let the variable be in the model¶

R-squared (0.751 ~ 75.1%) and Adj. R-squared (0.750 ~ 75%) are pretty high (closer to 1 better the model) and very close to each other. It shows that our independent variables can explain about 75% of the variance of dependent variable (charges)¶

Now we will check for Multicollinearity¶

We will use VIF to check for multicollinearity¶

VIFs are fine since all of them are less than 2¶

(Usually VIF threshold is taken as something between 2 - 3)¶

Predicting the price for the test data¶

Calculate the accuracy of the model¶

MAPE of 42.14% means the predicted values are 42.14% deviated from the actual values. We can assume this model has an accuracy of 100%- 42.14% = 57.86% of accuracy. This is rather poor accuracy.¶

Now we will be using Support Vector Machine (SVM)¶

We will do the feature scaling first¶

Predict the charges¶

Calculate MAPE¶

Method 1 - directly with in built function from scikit learn¶

Method 2 - manually by creating a data frame¶

We are getting a mape of 103% (absolutely not acceptable) which means Support Vector Regression (SVR) is not suitable for this data.¶

We will try with the hyper parameter tuning and try to improve the mape¶

optimal hyper-parameters¶

Calculate MAPE after hyper-parameters tuning¶

We can see that the mape has improved but still it's very high and not acceptable.¶

Now we will be using Random Forest algorithm¶

Predict the charges¶

Calculate MAPE¶

Method 1 - directly with in built function from scikit learn¶

Method 2 - manually by creating a data frame¶

We are getting a mape of 33%, it seems that Random Forest has performed the best among all the 3 algorithms¶

Now let's try again with the hyper-parameters if MAPE can be further improved¶

Predict and Calculate MAPE¶

We can see that mape has been brought down to 29%.¶

This is how we can fine tune the models to improve the accuracy.¶

You may check out all our instructor led courses from this link. https://www.analyticseducator.com/Courses-Offers.html¶

If you want to read more such Machine Learning case studies then you may go through the following links -¶

https://www.analyticseducator.com/Blog/Logistic-Regression_Titanic-Survival-checkpoint.html¶

https://www.analyticseducator.com/Blog/Cancer-Classification-Support-Vector-Machines.html¶

https://www.analyticseducator.com/Blog/K-Nearest%20Neighbours%20for%20T-shirt%20size%20classification.html¶

You may check out all our instructor led courses from this link. https://www.analyticseducator.com/Courses-Offers.html ¶

https://www.analyticseducator.com/Blog/Logistic-Regression_Titanic-Survival-checkpoint.html ¶

https://www.analyticseducator.com/Blog/Cancer-Classification-Support-Vector-Machines.html ¶

https://www.analyticseducator.com/Blog/K-Nearest%20Neighbours%20for%20T-shirt%20size%20classification.html ¶