Suppose You Are Interested in Determining the Factors That Determine $Crime~ \hat{per }~Student = 35 - 15$

Suppose you are interested in determining the factors that determine the number of crimes committed on campus.To this end,you collect data from 75 colleges on number of crimes per students enrolled,number of police officers per students,unemployment rate,tuition,and the percentage of male students.You run a regression and obtain the following results $Crime~ \hat{per }~Student = 35 - 15$ Police per Student $- .24$ Tuition
(13) (4) $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$ (.07)
$+ 3$ Unemployment Rate $+ 8$ Percent Male
$( 2.5 )$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$ (5)
$$\begin{array} { c } \mathrm { n } = 75 \\\mathrm { R } ^ { 2 } = .2305\end{array}$$
a)Which of the coefficient estimates are statistically significant at the 5% level?
b)You run an additional regression in order to jointly test if two coefficients are equal to 0.State the hypothesis,calculate the test statistic,state the regression rule,and state your decision. $Crime~ \hat{per} Student= 33 - 18$ Police per Student $- .35$ Tuition
$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$ (12) (3) $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~( .05 )$
$$\begin{aligned}\mathrm { n } & = 75 \\\mathrm { R } ^ { 2 } & = .2134\end{aligned}$$