Description
In this assignment, we will implement a number of linear models (including linear regression) to model relationships between
different clinical features for heart failure in patients.
For the dataset, we use ”heart failure clinical records data set
at UCI:
https://archive.ics.uci.edu/ml/datasets/Heart+failure+
clinical+records
Dataset Description: From the website: ”This dataset
contains the medical records of 299 patients who had heart failure, collected during their follow-up period, where each patient
profile has 13 clinical features.”
These 13 features are:
1. age: age of the patient (years)
2. anaemia: decrease of red blood cells or hemoglobin (boolean)
3. high blood pressure: if the patient has hypertension (boolean)
4. creatinine phosphokinase (CPK): level of the CPK enzyme
in the blood (mcg/L)
5. diabetes: if the patient has diabetes (boolean)
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BU MET CS-677: Data Science With Python, v.2.0 CS-677 Assignment: Linear Models
6. ejection fraction: percentage of blood leaving the heart at
each contraction (percentage)
7. platelets: platelets in the blood (kiloplatelets/mL)
8. sex: woman or man (binary)
9. serum creatinine: level of serum creatinine in the blood
(mg/dL)
10. serum sodium: level of serum sodium in the blood (mEq/L)
11. smoking: if the patient smokes or not (boolean)
12. time: follow-up period (days)
target death event: if the patient deceased (DEATH EVENT =
1) during the follow-up period (boolean)
We will focus on the following subset of four features:
1. creatinine phosphokinase
2. serum creatinine
3. serum sodium
4. platelets
and try establish a relationship between some of them using
various linear models and their variants.
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BU MET CS-677: Data Science With Python, v.2.0 CS-677 Assignment: Linear Models
Question 1:
1. load the data into Pandas dataframe. Extract two dataframes
with the above 4 features: df 0 for surviving patients (DEATH EVENT
= 0) and df 1 for deceased patients (DEATH EVENT = 1)
2. for each dataset, construct the visual representations of
correponding correlation matrices M0 (from df 0) and M1
(from df 1) and save the plots into two separate files
3. examine your correlation matrix plots visually and answer
the following:
(a) which features have the highest correlation for surviving
patients?
(b) which features have the lowest correlation for surviving
patients?
(c) which features have the highest correlation for deceased
patients?
(d) which features have the lowest correlation for deceased
patients?
(e) are results the same for both cases?
Question 2: In this question you will compare a number of
different models using linear systems (including linear regression). You choose one feature X as independent variable X
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BU MET CS-677: Data Science With Python, v.2.0 CS-677 Assignment: Linear Models
and another feature Y as dependent. Your choice of X and Y
will depend on your facilitator group as follows:
1. Group 1: X: creatinine phosphokinase (CPK), Y : platelets
2. Group 2: X: platelets, Y : serum sodium
3. Group 3: X: serum sodium, Y : serum creatinine
4. Group 4: X: platelets, Y : serum creatinine
We will now look for the best model (from the list below) that
best explains the relationship for surviving and deceased patients. Consider surviving patients (DEATH EVENT = 0).
Extract the corresponding columns for X and Y . For each
of the models below, we will take 50/50 split, fit model with
Xtrain and predict Ytest using Xtest. From the predicted values Pred(yi) we compute the residuals ri = yi − Pred(yi). We
can then estimate the loss function (SSE sum of the squared of
residuals)
L =
X
xi∈Xtest
e
2
i
You do the same analysis for deceased patients. You will consider the following models for both deceased and surviving patients:
1. y = ax + b (simple linear regression)
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BU MET CS-677: Data Science With Python, v.2.0 CS-677 Assignment: Linear Models
2. y = ax2 + bx + c (quadratic)
3. y = ax3 + bx2 + cx + d (cubic spline)
4. y = a log x + b (GLM – generalized linear model)
5. log y = a log x + b (GLM – generalized linear model)
For each of the model below, you will do the following (for both
deceased and surviving patients)
(a) fit t he model on Xtrain
(b) print the weights (a, b, . . .)
(c) compute predicted values using Xtest
(d) plot (if possible) predicted and actual values in Xtest
(e) compute (and print) the corresponding loss function
Question 3: Summarize your results from question 2 in a
table like shown below:
Model SSE (death event=0) (death event=1)
y = ax + b
y = ax2 + bx + c
y = ax3 + bx2 + cx + d
y = a log x + b
log y = a log x + b
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BU MET CS-677: Data Science With Python, v.2.0 CS-677 Assignment: Linear Models
1. which model was the best (smallest SSE) for surviving patients? for deceased patients?
2. which model was the worst (largest SSE) for surving patients? for deceased patients?
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