All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)

(ii)
(a) $r = 0.9860$
(b) $r = 0.9907$

(iii) Since the product moment correlation coefficient is close to 1 for (ib), the model $F = c+ dv^2$ is the better model.

(iv) From GC, the regression line of F on $v^2$ is

$F = 0.024242v^2 + 3.1957$

$F = 0.0242v^2 + 3.20$ (3SF)

When $F=26, 26 = 0.024242v^2 + 3.1957$

$\Rightarrow v = 30.7$

Since $v$ is the independent or controlled variable, neither the regression line of $v \text{~on~} F$ nor the regression line of $v^2 \text{~on~} F$ should be used.