Question

compute standard error of estimate for data below
x values= 3,-2,2,5,10
y values= 4,6,-2,0,-3

Answer 1

Conditions

compute standard error of estimate for data below

x values=3,-2,2,5,10

y values= 4,6,-2,0,-3

Solution

The formula for calculation of standard error:

$$SE = \frac{\sigma}{\sqrt{n}}$$

where

$$\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2}, \quad \text{where} \quad \mu = \frac{1}{N} \sum_{i=1}^{N} x_i.$$ $$\mu_x = \frac{1}{5} (3 - 2 + 2 + 5 + 10) = 3,6$$ $$\mu_y = \frac{1}{5} (4 + 6 - 2 + 0 - 3) = 1$$ $$\sigma_x = \sqrt{\frac{1}{5} \left( (3 - 3,6)^2 + (-2 - 3,6)^2 + (2 - 3,6)^2 + (5 - 3,6)^2 + (10 - 3,6)^2 \right)} =$$ $$= \sqrt{\frac{1}{5} \left( 0.36 + 31,36 + 2,56 + 1,96 + 40,96 \right)} = \sqrt{15,44} \approx 3,929$$ $$\sigma_y = \sqrt{\frac{1}{5} \left( (4 - 1)^2 + (6 - 1)^2 + (-2 - 1)^2 + (0 - 1)^2 + (-3 - 1)^2 \right)} =$$ $$= \sqrt{\frac{1}{5} (9 + 25 + 9 + 1 + 16)} = \sqrt{12} = 2\sqrt{3}$$ $$SE_x = \frac{3,929}{\sqrt{5}} \approx 1,757$$ $$SE_y = \frac{2\sqrt{3}}{\sqrt{5}} \approx 1,549$$