AWS SageMaker Tutorial: Part 3

Intro​

In this tutorial we will use multiple linear regression to predict health insurance cost for individuals based on multiple factors (age, gender, BMI, # of children, smoking and geo-location)

Investopedia: Multiple Linear Regression

Import Libraries​

``import pandas as pdimport numpy as npimport seaborn as snsimport matplotlib.pyplot as plt``

``# read the csv fileinsurance_df = pd.read_csv('insurance.csv')``

Check for Null Values​

``# check if there are any Null valuesinsurance_df.isnull().sum()``

Check DataFrame Info​

``# Check the dataframe infoinsurance_df.info()``

Grouping Data​

We can group our data with the .groupby() function

``# Grouping by region to see any relationship between region and charges# Seems like south east region has the highest charges and body mass indexdf_region = insurance_df.groupby(by='region').mean()df_region``

List Unique Values​

It's actually an array of unique values but...

``# Check unique values in the 'sex' columninsurance_df['sex'].unique()``

Convert Strings To Numbers​

Convert Categorical Variables (boolean) to numerical​

We must convert all string based data to numerical data or else we will encounter an error later when we convert everything to float32 format

pandas: .apply()

towardsdatascience.com: apply and lambda usage in pandas

``# convert categorical variable to numericalinsurance_df['sex'] = insurance_df['sex'].apply(lambda x: 0 if x == 'female' else 1)``

Dummies​

Convert all of our string options into a matrix of numerical indicator variables

pandas.get_dummies()

``region_dummies = pd.get_dummies(insurance_df['region'], drop_first = True)``

Replace Region Column w/ Region Dummies​

Now that we have turned our region string column into a matrix of booleans we need to concat the matrix onto the end of the datafield and then remove the region column

Concat Dummies​

``insurance_df = pd.concat([insurance_df, region_dummies], axis = 1)``

Delete Column (Drop Column)​

Rows and Columns can be deleted with the `.drop()` method.

pandas.drop()

``# Let's drop the original 'region' columninsurance_df.drop(['region'], axis = 1, inplace = True)``

Visualize The Dataset​

Now that we have normalized our data, let's create a series of histograms for each parameter.

``insurance_df[['age', 'sex', 'bmi', 'children', 'smoker', 'charges']].hist(bins = 30, figsize = (20,20), color = 'r')``

Regression Line Without Machine Learning​

We now have our data shaped into a format that we can use Seaborn to create a regression line without any machine learning. Let's go ahead and do that.

Here is the linear regression for Age

``sns.regplot(x = 'age', y = 'charges', data = insurance_df)plt.show()``

Here is the linear regression for BMI

``sns.regplot(x = 'bmi', y = 'charges', data = insurance_df)plt.show()``

Correlation Matrix Heatmap​

We can create a correlation matrix and then convert that to a heatmap to read it more easily

``corr = insurance_df.corr()corr``

``# resize heatmap so it is legibleplt.figure(figsize = (10,10))sns.heatmap(corr, annot = True)``

And with this correlation matrix heatmap we can see that the factor with the most correlation to insurance cost is whether or not a person is a smoker.

Create Training and Testing Dataset​

Separate Independent and Dependent Variables​

Now let's shape our data into training and testing data sets. Let's start by separating our independent variables from our dependent variables.

``X = insurance_df.drop(columns =['charges'])y = insurance_df['charges']``

And then we can review our new variables

Convert to float32 format​

The documentation states that we must convert all numbers to float32 format for regression analysis so lets do that.

``X = np.array(X).astype('float32')y = np.array(y).astype('float32')``

After we have converted to float32 let us reshape y so that it has a column

Split Into Train and Test Data​

``from sklearn.model_selection import train_test_splitX_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.2, random_state=42)``

The `random_state` here controls the shuffling applied to the data before applying the split. Pass an int for reproducible output across multiple function calls.

📘 sklearn: train_test_split

Scale the Data​

In short, the reason why we must scale our data is so that all our features are roughly using the same scale. If a feature has a variance that is orders of magnitude larger that others, it might dominate the objective function and make the estimator unable to learn from other features correctly as expected.

This is not necessary for single feature linear regression because there is only one feature. However this IS required for multiple linear regression.

Data that has been scaled is referred to as normalized data

📘 sklearn: StandardScaler

``#scaling the data before feeding the modelfrom sklearn.preprocessing import StandardScaler, MinMaxScalerscaler_x = StandardScaler()X_train = scaler_x.fit_transform(X_train)X_test = scaler_x.transform(X_test)scaler_y = StandardScaler()y_train = scaler_y.fit_transform(y_train)y_test = scaler_y.transform(y_test)``

Train and Test Linear Regression Model in SK-Learn​

Note that we are not using SageMaker Algorithms yet. This is a standard SK-Learn model.

``# using linear regression modelfrom sklearn.linear_model import LinearRegressionfrom sklearn.metrics import mean_squared_error, accuracy_scoreregresssion_model_sklearn = LinearRegression()regresssion_model_sklearn.fit(X_train, y_train) # highlight-line``

In the highlighted line we have fit the line

`regression_model_sklearn` now contains the trained parameters

``LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)``

Test Accuracy​

Now we can get an accuracy score

``regresssion_model_sklearn_accuracy = regresssion_model_sklearn.score(X_test, y_test)regresssion_model_sklearn_accuracy``
``0.7835929775784993``

So we have achieved about 78% accuracy.

Use Test Data to predict y​

Now we can feed in our X_test data that we set aside earlier to get an array of y predictions.

``y_predict = regresssion_model_sklearn.predict(X_test)y_predict``

And we can see that we get an array back, however all these numbers look a little small for insurance costs don't they? Well remember that earlier we normalized this data by scaling it down.

Scale Data Back Up (inverse transform)​

And we can see that when we use the inverse transform method of our scaler we get numbers in the range of what we would expect.

``y_predict_orig = scaler_y.inverse_transform(y_predict)y_predict_orig``

Calculating the Metrics​

We can now calculate some of the metrics that we covered in Ncoughlin: Regression Metrics and KPI's

``from sklearn.metrics import r2_score, mean_squared_error, mean_absolute_errorfrom math import sqrtRMSE = float(format(np.sqrt(mean_squared_error(y_test_orig, y_predict_orig)),'.3f'))MSE = mean_squared_error(y_test_orig, y_predict_orig)MAE = mean_absolute_error(y_test_orig, y_predict_orig)r2 = r2_score(y_test_orig, y_predict_orig)adj_r2 = 1-(1-r2)*(n-1)/(n-k-1)``

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