Given that $s _ { x } ^ { 2 } = 500 , s _ { y } ^ { 2 } = 750 , \operatorname { cov } ( x , y ) = 100$ and n = 6,the standard error of estimate is:
A) 3,749.00
B) 937.25
C) 30.21
D) None of these choices.

Question

Quizplus · Accepted Answer

The formula for the standard error of estimate (SEE) is:

$$SEE = \sqrt{\frac{s_y^2 - r^2s_x^2}{n-2}}$$

where $r$ is the correlation coefficient between $x$ and $y$.

We are given that $s_x^2 = 500$, $s_y^2 = 750$, $\operatorname{cov}(x,y) = 100$, and $n = 6$. We can use these values to calculate $r$:

$$r = \frac{\operatorname{cov}(x,y)}{s_x s_y} = \frac{100}{\sqrt{500\cdot 750}} \approx 0.4082$$

Now we can plug in all the values to get the SEE:

$$SEE = \sqrt{\frac{750 - 0.4082^2 \cdot 500}{6-2}} \approx 30.21$$

Therefore, the best choice is C.

Given That sx2=500,sy2=750,cov⁡(x,y)=100s _ { x } ^ { 2 } = 500 , s _ { y } ^ { 2 } = 750 , \operatorname { cov } ( x , y ) = 100sx2​=500,sy2​=750,cov(x,y)=100

Given That $s _ { x } ^ { 2 } = 500 , s _ { y } ^ { 2 } = 750 , \operatorname { cov } ( x , y ) = 100$