Untitled

| Step                  | Matrix Operation                  | Description                                                         |
|-----------------------|------------------------------------|---------------------------------------------------------------------|
| 1. Compute \(X'X\)    | \(\mathbf{X'X}\)                 | Multiply the transpose of \(X\) with \(X\) to form a \(k \times k\) matrix. |
| 2. Compute \(X'y\)    | \(\mathbf{X'y}\)                 | Multiply the transpose of \(X\) with \(y\) to form a \(k \times 1\) vector. |
| 3. Invert \(X'X\)     | \(\mathbf{(X'X)^{-1}}\)          | Compute the inverse of \(X'X\), ensuring it has full rank and is non-singular. |
| 4. Solve for \(\hat{\beta}\) | \(\mathbf{\hat{\beta} = (X'X)^{-1}X'y}\) | Multiply the inverse of \(X'X\) by \(X'y\) to estimate the coefficients (\(\beta\)). |
| Step                  | Matrix Operation                  | Description                                                         |
|-----------------------|------------------------------------|---------------------------------------------------------------------|
| 1. Compute \(X'X\)    | \(\mathbf{X'X}\)                 | Multiply the transpose of \(X\) with \(X\) to form a \(k \times k\) matrix. |
| 2. Compute \(X'y\)    | \(\mathbf{X'y}\)                 | Multiply the transpose of \(X\) with \(y\) to form a \(k \times 1\) vector. |
| 3. Invert \(X'X\)     | \(\mathbf{(X'X)^{-1}}\)          | Compute the inverse of \(X'X\), ensuring it has full rank and is non-singular. |
| 4. Solve for \(\hat{\beta}\) | \(\mathbf{\hat{\beta} = (X'X)^{-1}X'y}\) | Multiply the inverse of \(X'X\) by \(X'y\) to estimate the coefficients (\(\beta\)). |
| Step                  | Matrix Operation                  | Description                                                         |
|-----------------------|------------------------------------|---------------------------------------------------------------------|
| 1. Compute \(X'X\)    | \(\mathbf{X'X}\)                 | Multiply the transpose of \(X\) with \(X\) to form a \(k \times k\) matrix. |
| 2. Compute \(X'y\)    | \(\mathbf{X'y}\)                 | Multiply the transpose of \(X\) with \(y\) to form a \(k \times 1\) vector. |
| 3. Invert \(X'X\)     | \(\mathbf{(X'X)^{-1}}\)          | Compute the inverse of \(X'X\), ensuring it has full rank and is non-singular. |
| 4. Solve for \(\hat{\beta}\) | \(\mathbf{\hat{\beta} = (X'X)^{-1}X'y}\) | Multiply the inverse of \(X'X\) by \(X'y\) to estimate the coefficients (\(\beta\)). |