12. We want to know if there is a strong correlation between the square footage ($F$) of a house and the price ($P$) of a house.
(a) Find the equation of the regression line for $F$ vs. $P$, where $F$ is the independent variable (think $x$).
(b) Interpret the slope.
(c) Find $r$ and (using $r$) explain if there a significant linear relationship between $F$ and $P$.
(d) Using the regression line, predict the cost of a 1,600 ft$^2$ house. Find the residual.
(e) Using the regression line, predict the cost of a 3,500 ft$^2$ house. Was this interpolation or extrapolation?
(f) Using the regression line, you can see a house of size 100 square feet will have a negative price, which does not make sense. What's the smallest house that will have a positive price?
(g) Compute the correlation coefficient between $F$ and $B$. Is there a stronger correlation between (i) $F$ and $P$ or (ii) $F$ and $B$?