How does the t-value for the sample correlation coefficient r compare to the t-value for the corresponding slope b of the sample least-squares line

Respuesta :

[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?

  • slope, Numerical measure of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).
  • Generally, the slope of a line gives the measure of its steepness and direction.

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]

Learn more about slope

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