$In todays class professor discussed about given equation,$

y=b0+b1X1+b2X2+b3X3+E(error)

In this equation:

- $y$ represents the dependent variable or the target you are trying to predict.
- $X_{1},X_{2},$ and $X_{3}$ are independent variables or predictors.
- $b_{0},b_{1},b_{2},$ and $b_{3}$ are the coefficients of the respective predictors.
- $E$ represents the error term, which accounts for the variability in $y$ that cannot be explained by the predictors.

**Linear Relationship**: This equation still assumes a linear relationship between the dependent variable ($y$) and the independent variables ($X_{1},X_{2},$ and $X_{3}$). Each coefficient ($b_{1},b_{2},$ and $b_{3}$) represents the change in $y$ for a one-unit change in the corresponding predictor, assuming all other predictors remain constant.**Overfitting**: The risk of overfitting still applies in multiple linear regression, particularly if you have a high number of predictors relative to your sample size. Including too many predictors without enough data can lead to overfitting, just like in polynomial regression.**Model Evaluation**: To assess the performance of this multiple linear regression model, you can use techniques such as R-squared (coefficient of determination), p-values for the coefficients, and residual analysis to ensure the model’s validity.**Regularization**: In cases where you have many predictors or suspect multicollinearity (correlation between predictors), you may consider using regularization techniques like Ridge or Lasso regression to prevent overfitting and improve model generalization.**Interpretation**: Interpretation of coefficients ($b_{1},b_{2},$ and $b_{3}$) remains the same as in simple linear regression. Each coefficient tells you the effect of a one-unit change in the corresponding predictor on the dependent variable, holding other predictors constant.**Assumptions**: Like in simple linear regression, multiple linear regression assumes that the errors ($E$) are normally distributed, have constant variance (homoscedasticity), and are independent of each other (no autocorrelation).