Chapter 2: Linear Regression

## What is Linear Regression?

Linear Regression is one of the simplest and most widely used supervised learning algorithms.
It models the relationship between one or more independent variables (features) and a continuous dependent variable (target) by fitting a linear equation to observed data.

## Why Linear Regression?
- Easy to interpret — coefficients show how each feature affects the outcome.
- Fast to train and predict.
- Good baseline model for continuous biomedical outcomes.

## Biomedical Applications of Linear Regression
### 1. Predicting Blood Pressure
Using patient data such as age, weight, and cholesterol levels to predict systolic blood pressure.

### 2. Estimating Disease Progression
Modeling how biomarkers change over time to estimate progression rate in diseases like diabetes or Parkinson’s.

### 3. Dosage Optimization
Predicting the right medication dose based on patient-specific factors (weight, age, kidney function).

## Example: Predicting Blood Pressure
Suppose we have data on patients’ age and weight, and their measured blood pressure. Linear regression can find the relationship:

## Assumptions of Linear Regression

- Linear relationship between features and outcome.
- Residuals (errors) are normally distributed.
- Homoscedasticity: constant variance of errors.
- No multicollinearity (independent features).

## Limitations
- Cannot capture complex nonlinear relationships.
- Sensitive to outliers.
- Assumes independence of observations.

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**Next chapter:** Logistic Regression  
(We’ll learn about classifying biomedical data — for example, determining if a patient has a disease or not.)