The standard error formula

Solution

False.

\[SE\left( b_2 \right)=\sqrt{\widehat{Var}\left( b_2 \right)}=\sqrt{ \frac{s^2}{\sum_{i=1}^{n}{ {\left( x_i-\bar{x} \right)}^2 }}}= \frac{\sqrt{s^2}}{\sqrt{\sum_{i=1}^{n}{ {\left( x_i-\bar{x} \right)}^2 }}}= \frac{s}{\sqrt{\sum_{i=1}^{n}{ {\left( x_i-\bar{x} \right)}^2 }}}\]

but

\[\sqrt{\sum_{i=1}^{n}{ {\left( x_i-\bar{x} \right)}^2 }}≠\sum_{i=1}^{n}{ \sqrt{{\left( x_i-\bar{x} \right)}^2} }=\sum_{i=1}^{n}{ \left( x_i-\bar{x} \right) }\]

for the same reason that

\[\sqrt{a+b}≠\sqrt{a}+\sqrt{b}\]