Problem $3$: Heart Disease Dataset

In Problem $3,$ you will be working with the Statlog Heart Disease Dataset. This dataset contains medical information about

$270$ individuals, including a column that indicates whether or not the individual has heart disease. You can find more about

this dataset, including descriptions of its columns, here: Statlog Heart Dataset.

Load the data stored in the tab$-$delimited file heart$\_$disease.txt into a DataFrame named hd$.$ Use head$()$ to display

the first $10$ rows of this DataFrame.

Our goal in this problem will be to create a logistic regression model to predict the label heart$\_$disease using the other

columns as features. Note that a value of $1$ in the heart$\_$disease column indicates an absence of heart disease, while a

value of $2$ indicates the presence of heart disease.

Perform the following steps in a single code cell:

$$ Create a $2$D feature array named X$3$ containing the relevant features, as well as a $1$D label array named y$3$

containing the labels. $($Note: These should be arrays, and not DataFrames or Series.$)$

$$ Use train$\_$test$\_$split$()$ to split the data into training and testing sets using an $80/20$ split. Name the

resulting arrays X$\_$train$\_3,$ X$\_$test$\_3,$ y$\_$train$\_3,$ and y$\_$test$\_3.$ Set random state$=1.$ Use stratified

sampling.

$$ Print the shapes of X$\_$train$\_3$ and X$\_$test$\_3.$ Include text labeling the two results as shown below. Add

spacing to ensure that the shape tuples are left$-$aligned.

Training Features Shape: xxxx

Test Features Shape: xxxx

$5$

We will now create a logistic regression model that can be used to estimate the probability that an individual has heart

disease based on the feature values.

Create a logistic regression model named hd$\_$mod with solver$=\text{'}$lbfgs$\text{'}$ and penalty$=$'none'. Then fit the model

to the training data. If you get a warning message stating that the model failed to converge, then increase the max$\_$iter

parameter until it does converge.

Display the intercepts and coefficients for the final model with text labels as shown below. Note that the coefficients

array will not fit on a single line, so please display it BENEATH the line containing the "Coefficients:" label.

Intercept: xxxx

Coefficients:

xxxx

We will now calculate the accuracy score for the model on both the training set and the test set.

Calculate and print the training and testing accuracy scores for your model, rounded to four decimal places. Include the

text labels explaining which value is which, as shown below. Add spacing to ensure that the scores are left$-$aligned.

Training Accuracy: xxxx

Testing Accuracy: xxxx

We will now use the model to generate predictions regarding the presence or absence of heart disease for individuals in the

test set.

Use your model to generate label predictions for observations in the test set. Store the results in a variable named

test$\_$pred$\_3.$ Print the first $20$ observed labels for the test set, and then the first $20$ predicted labels. Include text

labels with your output as shown below. Each label array should be displayed on a single line, and the two arrays should

be left$-$aligned.

Observed Labels: xxxx

Predicted Labels: xxxx

As a final step, we will use our model to estimate the probability that each individual in the test set has heart disease.

Use the predict$\_$proba$()$ method of your model to estimate probabilities of being in each of the two classes for each

individual in the test set. This function returns a $2$D array. Display the predicted probabilities for the first $10$ observations

in the test set as a DataFrame with the columns named according to the labels that they represent $(1$ and $2).$