Differences

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--- regression [2019/12/06 08:25] – hkimscil
+++ regression [2020/11/05 17:40] – [E.g., 3. Simple regression: Adjusted R squared & Slope test] hkimscil
@@ Line 748: / Line 748: @@
    * $\displaystyle t=\frac{b_{1}}{s_{b_{1}}}$
-   * $\displaystyle s_{b_{1}} = \frac {MSE}{SS_{X}} = \frac{\sqrt{\frac{SSE}{n-2}}}{\sqrt{SS_{X}}} = \display\frac{\sqrt{\frac{\Sigma{(Y-\hat{Y})^2}}{n-2}}}{\sqrt{\Sigma{(X_{i}-\bar{X})^2}}} $
+   * $\displaystyle s_{b_{1}} = \frac {MSE}{SS_{X}} = \frac{\sqrt{\frac{SSE}{n-2}}}{\sqrt{SS_{X}}} = \displaystyle \frac{\sqrt{\frac{\Sigma{(Y-\hat{Y})^2}}{n-2}}}{\sqrt{\Sigma{(X_{i}-\bar{X})^2}}} $
 ^ X  ^ Y  ^ $X-\bar{X}$  ^ ssx  ^ sp  ^ y<sub>predicted</sub>  ^ error  ^ error<sup>2</sup>  ^
@@ Line 761: / Line 761: @@
 SSE = Sum of Square Error
 기울기 beta(b)에 대한 표준오차값은 아래와 같이 구한다.
-$$se_{\beta} = \frac {\sqrt{SSE/n-2}}{\sqrt{SSX}} \\
+\begin{eqnarray*}
- & = &  \frac {\sqrt{1.1/3}}{\sqrt{10}} = 0.191485 $$
+se_{\beta} = \frac {\sqrt{SSE/n-2}}{\sqrt{SSX}} \\
+& = & \frac {\sqrt{1.1/3}}{\sqrt{10}}  \\
+& = & 0.191485
+\end{eqnarray*}
 그리고 b = 0.7
 따라서 t = b / se = 3.655631