[tex]= \ \frac{\beta _{1}}{s\beta _{1} } = t\beta _{1}[/tex] the t-value for the sample correlation coefficient r compare to the t-value .
What is the slope in math?
The two t values are equal.
[tex]t_{r} = r \frac{\sqrt{n - 2} }{\sqrt{1 - r^{2} } }[/tex]
[tex]= \frac{r * \sqrt{SST / \sqrt{SSR} } }{(\sqrt{1 - r^{2}) * \sqrt{SST} /\sqrt{SSR/(n - 2)} } }[/tex]
[tex]= \ \frac{\beta _{1}}{s\beta _{1} } = t\beta _{1}[/tex]
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