Given that cov(x,y) = 10, $s _ { y } ^ { 2 }$ = 15, $S _ { x } ^ { 2 }$ = 8 and n = 12, the value of the standard error of estimate, $S _ { \varepsilon }$ , is 2.75.

Question

Quizplus · Accepted Answer

The standard error of estimate, $S_{\varepsilon}$, is calculated using the formula $S_{\varepsilon} = \sqrt{\frac{1}{n-2} \left( S_y^2 - \frac{cov(x,y)^2}{S_x^2} \right)}$. Substituting the given values, $S_{\varepsilon} = \sqrt{\frac{1}{12-2} \left( 15 - \frac{10^2}{8} \right)} = \sqrt{\frac{1}{10} \left( 15 - \frac{100}{8} \right)} = \sqrt{\frac{1}{10} \left( 15 - 12.5 \right)} = \sqrt{\frac{2.5}{10}} = \sqrt{0.25} = 0.5$, not 2.75.

Given That Cov(x,y) = 10 sy2s _ { y } ^ { 2 }sy2​

Given That Cov(x,y) = 10 $s _ { y } ^ { 2 }$