Homelessness Is a Problem in Many Large U $F$ ) Dependent Variable Is Homeless

Essay

Homelessness is a problem in many large U.S. cities. To better understand the problem, a
multiple regression was used to model the rate of homelessness based on several
explanatory variables. The following data were collected for 50 large U.S. cities. The
regression results appear below. Homeless number of homeless people per 10,000 in a city Poverty percent of residents with income under the poverty line Unemployment percent of residents unemployed Temperature average yearly temperature (in degrees $F$ .)
$\begin{array} { l l } \text { Vacancy } & \text { percent of housing that is unoccupied } \\ \text { Rent Control indicator variable, } 1 = \text { city has rent control, } 0 = \text { no rent control } \end{array}$

Dependent variable is Homeless
$\mathrm { R }$ squared $= 38.4 \% \quad \mathrm { R }$ squared (adjusted) $= 31.5 \%$
$\mathrm { s } = 2.861$ with $50 - 6 = 44$ degrees of freedom


$\begin{array} { l c c r l } \text { Variable } & \text { Coeff } & \text { SE(Coeff) } & \text { t-ratio } & \text { p-value } \\ \text { Constant } & - 4.275 & 3.465 & - 1.23 & 0.2239 \\ \text { Poverty } & 0.0823 & 0.0823 & 1.00 & 0.3228 \\ \text { Unemployment } & 0.159 & 0.218 & 0.73 & 0.4699 \\ \text { Temperature } & 0.135 & 0.0587 & 2.30 & 0.0262 \\ \text { Vacancy } & - 0.247 & 0.138 & - 1.79 & 0.0809 \\ \text { Rent Control } & 2.944 & 1.37 & 2.15 & 0.0373 \end{array}$
a. Using a 5% level of significance, which variables are associated with the number of
homeless in a city?
b. Explain the meaning of the coefficient of temperature in the context of this problem.
c. Explain the meaning of the coefficient of rent control in the context of this problem.
d. Do the results suggest that having rent control laws in a city causes higher levels of
homelessness? Explain.
e. If we created a new model by adding several more explanatory variables, which statistic
should be used to compare them $$\text { - the } R ^ { 2 } \text { or the adjusted } R ^ { 2 } \text { ? Explain. }$$
f. Using the plots below, check the regression conditions.