Introduction to Machine Learning |
Multivariate linear regression is a statistical technique used for modeling the relationship between multiple independent variables and a dependent variable \(y\). In this approach, we aim to find a linear equation that best represents the relationship between the variables.
1. Prediction Equation:
\(y = \beta_0 + \beta_1x_1 + \beta_2x_2 + \ldots + \beta_nx_n\)
2. Loss Function:
\(L(\beta_0,\beta_1,\beta_2,\ldots,\beta_n) = \frac{1}{2n}\sum_{i=1}^n (y_i - (\beta_0 + \beta_1x_{1i} + \beta_2x_{2i} + \ldots + \beta_nx_{ni}))^2\)
3. Optimizing the Loss Function:
We can minimize \(L(\beta_0,\beta_1,\beta_2,\ldots,\beta_n)\) by taking partial derivatives with respect to \(\beta_0, \beta_1, \beta_2, \ldots, \beta_n\), and setting them to zero.
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