• Linear Regression is a widely used statistical technique for modeling relationships between a dependent variable and one or more independent variables.
• It is extensively applied in finance, healthcare, engineering, and machine learning.
• Helps in predicting continuous outcomes from input features.

• The equation for Simple Linear Regression: \[ Y = \beta_0 + \beta_1 X + \epsilon \]

  Where:

  • \(Y\) = Dependent Variable
  • \(X\) = Independent Variable
  • \(\beta_0\) = Intercept
  • \(\beta_1\) = Slope
  • \(\epsilon\) = Error Term

data <- data.frame(
  X = rnorm(100, mean = 5, sd = 2),
  Y = 3 + 2*rnorm(100, mean = 5, sd = 2) + rnorm(100, sd = 1)
)
head(data)

##          X         Y
## 1 7.741917 15.802932
## 2 3.870604 17.512782
## 3 5.726257 10.158491
## 4 6.265725 22.453467
## 5 5.808537  8.956045
## 6 4.787751 12.271200

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

## `geom_smooth()` using formula = 'y ~ x'

model <- lm(Y ~ X, data = data)
summary(model)$coefficients

##                Estimate Std. Error     t value     Pr(>|t|)
## (Intercept) 12.72265214  1.0155058 12.52839003 4.579201e-22
## X           -0.01637802  0.1855634 -0.08826103 9.298493e-01

• R-squared: Determines how well the model fits the data.
• Mean Squared Error (MSE): Measures the average squared difference between predicted and actual values.
• Residual Analysis: Identifies patterns in errors.

• Linear Regression is a fundamental technique for predictive modeling.
• Common applications include:
  • Stock Market Predictions (Finance)
  • Disease Risk Assessment (Healthcare)
  • Quality Control (Engineering)
• Future improvements include:
  • Polynomial Regression for complex relationships
  • Ridge & Lasso Regression for regularization
  • Machine Learning Approaches for advanced prediction models