Exercise $12$ The following is the regression result on a sample of $1000$ apartment houses in a

Japanese city $($standard errors in parentheses$)$:

widehat$($ rprice $)={71\mathrm{.}3}_{(9\mathrm{.}9)}+{1\mathrm{.}4}_{(0\mathrm{.}3)}*$ area $-{1\mathrm{.}9}_{(0\mathrm{.}5)}*$ age $+{0\mathrm{.}9}_{(0\mathrm{.}4)}*$ renov

where rprice is the monthly rental price $(1,000JPY),$ area is the area size $(m^2)$ of the house, age

is the age of the apartment $($years$),$ and renov is a dummy variable renov $=1$ if the apartment

underwent a renovation.

Suppose that an apartment owner renovates the apartment. What is the predicted increase$/$de$-$

crease in the rental price of a house in the apartment?

Suppose that, instead of measuring rprice and area in $1,000$JPY and $m^2,$ these variables

are measured in $100$JPY and $10m^2.$ What is the coefficient estimate of area from this new

regression?

Is the hypothesis renovated and un$-$renovated apartments have the same economic value re$-$

jected at the $5\%$ significance level? If yes $($no$),$ what about the significance level at $1\%(10\%)?$