Deriving Beta One and Beta Two in Multiple Regression Model

Step 1: Understand the Multiple Regression Model
- In a multiple regression model, we have multiple independent variables (X1, X2, X3, etc.) predicting a dependent variable (Y).
- The model equation is Y = beta0 + beta1*X1 + beta2*X2 + ... + error.

Step 2: Calculate Beta One (beta1)
- To calculate beta1, we need to minimize the sum of squared errors (SSE) by finding the partial derivative of SSE with respect to beta1 and setting it to zero.
- This involves taking the derivative of SSE with respect to beta1 and solving for beta1.

Step 3: Calculate Beta Two (beta2)
- Similarly, to calculate beta2, we repeat the process by finding the partial derivative of SSE with respect to beta2 and setting it to zero.
- This involves taking the derivative of SSE with respect to beta2 and solving for beta2.

Step 4: Interpret the Results
- Once we have calculated beta1 and beta2, we can interpret their values in relation to the dependent variable Y.
- Beta1 represents the change in Y for a one-unit change in X1, holding other variables constant.
- Beta2 represents the change in Y for a one-unit change in X2, holding other variables constant.