regression
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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 | ||
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r & = & \displaystyle \frac{SP}{\sqrt{SS_X SS_Y}}\text{, | r & = & \displaystyle \frac{SP}{\sqrt{SS_X SS_Y}}\text{, | ||
SP & = & r * \displaystyle \sqrt{SS_X SS_Y} \quad \text{and} \\ | SP & = & r * \displaystyle \sqrt{SS_X SS_Y} \quad \text{and} \\ | ||
+ | \\ | ||
b & = & \displaystyle \frac{SP}{SS_X} \\ | b & = & \displaystyle \frac{SP}{SS_X} \\ | ||
& = & \displaystyle \frac{r * \sqrt{SS_X SS_Y}}{SS_X} | & = & \displaystyle \frac{r * \sqrt{SS_X SS_Y}}{SS_X} | ||
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* $\displaystyle t=\frac{b_{1}}{s_{b_{1}}}$ | * $\displaystyle t=\frac{b_{1}}{s_{b_{1}}}$ | ||
- | * $\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 |
^ X ^ Y ^ $X-\bar{X}$ | ^ X ^ Y ^ $X-\bar{X}$ | ||
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SSE = Sum of Square Error | SSE = Sum of Square Error | ||
기울기 beta(b)에 대한 표준오차값은 아래와 같이 구한다. | 기울기 beta(b)에 대한 표준오차값은 아래와 같이 구한다. | ||
- | $$se_{\beta} = \frac {\sqrt{SSE/ | + | \begin{eqnarray*} |
- | & = & \frac {\sqrt{1.1/ | + | se_{\beta} = \frac {\sqrt{SSE/ |
+ | & = & \frac {\sqrt{1.1/ | ||
+ | & = & 0.191485 | ||
+ | \end{eqnarray*} | ||
그리고 b = 0.7 | 그리고 b = 0.7 | ||
따라서 t = b / se = 3.655631 | 따라서 t = b / se = 3.655631 |
regression.txt · Last modified: 2023/05/24 08:53 by hkimscil