Use the data in ATTEND for this exercise.$($i$)$In the model of Example $6\mathrm{.}3,$ argue that

Astndhl$$priGPA $=$ $,+2$$,$priGPA $+$ Beatdrte.

Use equation $(6,19)$ to estimate the partial effect when priGPA $=2\mathrm{.}59$ and adrte $=82.$Interpret your estimate.$)$Show that the equation can be written as

sindfn$!=0,+$B$,$atndre$+8,$priGPA$+$$,$ACT$+$B$.($priGPA$-2\mathrm{.}59)+$BACT'$+$ BpriGPA$($atndre$-82)+$ u$,$

where $8,=$ $,+2$$,(2.$$$9)+$ $,(82).($Note that the intercept has changed, but this is unim$-$portant.$)$ Use this to obtain the standard error of @$,$ from part $($i$).$Suppose that, in place ofpriGPA$($atndrte $-82).$ you put $($priGPA$-2\mathrm{.}59)($aindrte $-82).$G$)$Now how do you interpret the coefficients on atndrte and priGPA?