A random sample of $130$ male engineering students is obtained, and their heights are measured in $\text{inches}$ and in $\text{centimeters}$.
From the regression analysis, the predicted height in $\text{centimeters}$ for a student who is $70\text{ inches}$ tall is found to be $177.8\text{ cm}$. The sum of squared residuals from the regression is ${\text{42.25 cm}}^2$.
i. What is the value of the standard error of estimate (SE)?
ii. For a student whose height is $70\text{ inches}$, what is the $95\%$ prediction interval?

• A. i. $SE=0.46\text{ cm}$ii. $(176.45\text{ cm, }179.15\text{ cm)}$
• B. i. $SE=0.57\text{ cm}$ii. $(176.66\text{ cm, }178.94\text{ cm)}$
• C. i. $SE=0.46\text{ cm}$ii. $(176.45\text{ cm, }178.94\text{ cm)}$
• D. i. $SE=0.57\text{ cm}$ii. $(176.66\text{ cm, }179.15\text{ cm)}$

Answer: (B)