standard_error_of_regression_coefficient
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| standard_error_of_regression_coefficient [2026/05/30 07:12] – hkimscil | standard_error_of_regression_coefficient [2026/07/01 06:02] (current) – hkimscil | ||
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| & = & \dfrac {s_{e}} {\sqrt{ss(x)} } \\ | & = & \dfrac {s_{e}} {\sqrt{ss(x)} } \\ | ||
| & = & \dfrac {s_{e}} {\Sigma{(x_{i}-\overline{x})^2}} \\ | & = & \dfrac {s_{e}} {\Sigma{(x_{i}-\overline{x})^2}} \\ | ||
| - | & = & \dfrac {\dfrac{\sqrt {\text{ss(res)} }{n-2}} } {\sqrt{\Sigma{(x_{i}-\overline{x})^2}} } \\ | + | & = & \dfrac { \sqrt {\dfrac{ \Sigma{(y-\hat{y})^2} } {n-2} } } {\sqrt{\Sigma{(x_{i}-\overline{x})^2}} } \\ |
| - | & = & \dfrac {\dfrac{\Sigma{(y-\hat{y} )^2} }{n-2}} | + | & = & \sqrt {\dfrac { \dfrac { \Sigma {(y-\hat {y})^2 } } {n-2} } { \Sigma{(x_{i}-\overline{x})^2} } } \\ |
| \end{eqnarray*} | \end{eqnarray*} | ||
| Line 15: | Line 15: | ||
| \end{eqnarray*} | \end{eqnarray*} | ||
| + | ====== in Multiple Regression ====== | ||
| + | In multiple regression, the SE of a coefficient \(\beta _{j}\) is calculated using matrix algebra as | ||
| + | * $SE(\hat{\beta}_j) = \displaystyle \sqrt{s^2 \cdot C_{jj}}$, | ||
| + | * where $(s^{2})$ is the residual variance and | ||
| + | * $(C_{jj})$ is the corresponding diagonal element of the variance-covariance matrix $((X^TX)^{-1})$. | ||
| + | |||
| + | how to calculate standard error of regression coefficient in multiple regression | ||
standard_error_of_regression_coefficient.1780125177.txt.gz · Last modified: by hkimscil