$2$

R: rainfall $($inches$)$

T: temperature $($ F$)$

P: public transit utilization $($proportion of population commuting via public$).$

You perform the following regressions:

$($Eq $1)$

$U_i=100+25R_i+0\mathrm{.}05T_i+5P_i+$ er

$($Eq $2)$

$U_i=109+25\mathrm{.}2R_i+5\mathrm{.}5P_i+$ error ${?}_i$

$($Eq $3){?}_i=15+R_i+$ error ${?}_i$

$($Eq $4)T_i=51+10P_i+4R_i+$ error ${?}_i$

$($Eq $5)P_i=0\mathrm{.}65-0\mathrm{.}33R_i+$ error ${?}_i$

$($Eq $6)U_i=110+23\mathrm{.}4R_i+$ error ${?}_i$

$($a$)$ Using the OVB formulae we worked on in the Week $10$ lecture notes, the difference in the coefficient on $R$ in $Eq(1)$ and $Eq(2)$ equals to the product of two coefficients from the above regressions. Fill in the blanks in the following.

$25\mathrm{.}2-25=$