Multi Regression

The multiple regression model can be represented as follows:
Multiple Regression Equation:

Y = β₀ + β₁ * X₁ + β₂ * X₂ + ... + βₚ * Xₚ + ε

Formulas:
- β: Coefficients vector (β₀, β₁, β₂, ..., βₚ)
- X: Matrix of independent variables (including a column of ones for the intercept term)
- Y: Vector of the dependent variable
- ε: Error term (residuals)

Coefficient (β) Calculation:

β = (X^T X)^(-1) X^T Y

Where:
- X^T: Transpose of matrix X
- (X^T X)^(-1): Inverse of the matrix (X^T X)
- X^T Y: Dot product of X^T and Y

Note: The coefficient vector (β) represents the slope (β₁, β₂, ..., βₚ) for each independent variable and the y-intercept (β₀).

Once we have the values of β₀, β₁, β₂, ..., βₚ we can use the multiple regression equation Y = β₀ + β₁ * X₁ + β₂ * X₂ + ... + βₚ * Xₚ + ε to make predictions for new values of the independent variables.

To evaluate the performance of the multiple regression model, you can use various metrics like the coefficient of determination R2 or the mean squared error MSE.

Let's summarize the steps of multiple regression:

● Set up the multiple regression equation.
● Prepare the data by creating a matrix of independent variables (including a column of ones for the intercept term) and a vector of the dependent variable.
● Calculate the coefficients β using the formula given above
● Use the multiple regression equation to make predictions for new values of the independent variables.
● Evaluate the performance of the model using appropriate metrics.