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9.4: Correlation and Regression Formulas
https://stats.libretexts.org/Workbench/Statistics_for_Behavioral_Science_Majors/09%3A_Correlation_and_Regression/9.04%3A_Correlation_and_Regression_Formulas
$t = \frac{b_{1}}{\sqrt{ \left( \frac{MSE}{SS_{xx}} \right)}}$ $H_{1}: \beta_{1} \neq 0$ \(\hat{y} \pm t_{\alpha / 2} \cdot s_{est} \sqrt{\left( 1 + \frac{1}{n} + \frac{\left(x - \bar{x}\right)^{2... $t = \frac{b_{1}}{\sqrt{ \left( \frac{MSE}{SS_{xx}} \right)}}$ $H_{1}: \beta_{1} \neq 0$ $\hat{y} \pm t_{\alpha / 2} \cdot s_{est} \sqrt{\left( 1 + \frac{1}{n} + \frac{\left(x - \bar{x}\right)^{2}}{SS_{xx}} \right)}$ $\hat{y} = b_{0} + b_{1} x_{1} + b_{2} x_{2} + \cdot + b_{p} x_{p}$ $H_{0}: \beta_{1} = \beta_{2} = \cdots = \beta_{p} = 0$ $R_{adj}^{2} = 1 - \left( \frac{\left(1 - R^{2}\right) (n-1)}{(n - p - 1)} \right)$
4.6: Chapter 4 Formulas
https://stats.libretexts.org/Workbench/Introduction_to_Statistical_Methods_(Yuba_College)/04%3A_Correlation_and_Regression/4.06%3A_Chapter_4_Formulas
$t = \frac{b_{1}}{\sqrt{ \left( \frac{MSE}{SS_{xx}} \right)}}$ $H_{1}: \beta_{1} \neq 0$ \(\hat{y} \pm t_{\alpha / 2} \cdot s_{est} \sqrt{\left( 1 + \frac{1}{n} + \frac{\left(x - \bar{x}\right)^{2... $t = \frac{b_{1}}{\sqrt{ \left( \frac{MSE}{SS_{xx}} \right)}}$ $H_{1}: \beta_{1} \neq 0$ $\hat{y} \pm t_{\alpha / 2} \cdot s_{est} \sqrt{\left( 1 + \frac{1}{n} + \frac{\left(x - \bar{x}\right)^{2}}{SS_{xx}} \right)}$ $\hat{y} = b_{0} + b_{1} x_{1} + b_{2} x_{2} + \cdot + b_{p} x_{p}$ $H_{0}: \beta_{1} = \beta_{2} = \cdots = \beta_{p} = 0$ $R_{adj}^{2} = 1 - \left( \frac{\left(1 - R^{2}\right) (n-1)}{(n - p - 1)} \right)$

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