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--- standard_error_of_regression_slope [2022/10/13 12:18] – created hkimscil
+++ standard_error_of_regression_slope [2022/10/28 08:44] (current) – hkimscil
@@ Line 1: / Line 1: @@
 \begin{eqnarray*}
-\sqrt { \frac { \frac {\sum(Y_i - \hat{Y})^2)}  {n-2} } { \sum{(X_i - \overline{X})^2} } }
+\large {s(b_1)} & = &
-& = & \sqrt {\frac {\sum(Y_i - \hat{Y})^2)}
+\sqrt { \cfrac { \sum(y_i - \hat{y})^2 /  n-2 } { \sum{(x_i - \overline{x})^2} } } \\
-{
+& = & \sqrt { \cfrac {{ \cfrac{\text{SS}_{res}} {n-2} }} {\text{SS}_{X}}  } \\
-{{n-2} \sum{(X_i - \overline{X})^2} }
+& = & \sqrt { \cfrac {1}{{n-2}} \cdot \cfrac {\sum(y_i - \hat{y})^2}  { \sum{(x_i - \bar{x})^2} } } \\
-}
-}
 \end{eqnarray*}