Linear
Regression
Regression
Regression is a statistical method to model and analyze relationships between variables.
Types of Regression
Linear Regression: Simple (1 predictor) and Multiple (more than 1 predictor).
Logistic Regression, Polynomial Regression, etc.
Objectives of Regression
Predict outcomes based on predictor variables.
Understand the strength and direction of relationships.
Make informed decisions using models.
Linear Regression Model
- Simple Linear Regression Equation:
y=β0+β1x+ϵ
y = Dependent variable (outcome).
x = Independent variable (predictor).
β0 = Intercept.
β0 = Slope.
ϵ = Error term.
Assumptions of Linear Regression
Linearity: Relationship between x and y is linear.
Independence: Observations are independent.
Homoscedasticity: Errors have constant variance.
Normality: Residuals are normally distributed.
Practice GLM
General Explanation of Regression Metrics:
Intercept: The baseline prediction when all predictors are zero.
Coefficients: The change in the dependent variable for a one-unit increase in the predictor.
P-value: Determines statistical significance (p < 0.05 is typically significant).
R-squared: Explains the proportion of variance captured by the model (higher values indicate a better fit).
