Question

3. Let \textit{rent} be the average monthly rent, \textit{pop} the total city population, \textit{avginc} the average city income, and \textit{pctstu} the student population as a percentage of the total population. One model to test for a relationship is $\ln(\text{rent}) = \beta_0 + \beta_1 \ln(\text{pop}) + \beta_2 \ln(\text{avginc}) + \beta_3 \text{pctstu} + u$ and the estimated equation is $\widehat{\ln(\text{rent})} = 0.043 + 0.066 \ln(\text{pop}) + 0.507 \ln(\text{avginc}) + 0.006 \text{pctstu}$ $\qquad (0.844) \quad (0.039) \qquad \qquad (0.081) \qquad \qquad (0.002)$ $n = 64 \quad R^2 = 0.458$ (a) (10%) State the null and alternative hypotheses that, other factors being equal, the elasticity of rent with respect to \textit{pop} is different from zero. (b) (5%) Test the null hypothesis stated in (a) at the 10% level. (c) (5%) Test the null hypothesis stated in (a) at the 5% level. (d) (5%) Find the 95% confidence interval associated with the null hypothesis stated in (a).

          3. Let \textit{rent} be the average monthly rent, \textit{pop} the total city population, \textit{avginc} the average city income, and \textit{pctstu} the student population as a percentage of the total population. One model to test for a relationship is
$\ln(\text{rent}) = \beta_0 + \beta_1 \ln(\text{pop}) + \beta_2 \ln(\text{avginc}) + \beta_3 \text{pctstu} + u$
and the estimated equation is
$\widehat{\ln(\text{rent})} = 0.043 + 0.066 \ln(\text{pop}) + 0.507 \ln(\text{avginc}) + 0.006 \text{pctstu}$
$\qquad (0.844) \quad (0.039) \qquad \qquad (0.081) \qquad \qquad (0.002)$
$n = 64 \quad R^2 = 0.458$
(a) (10%) State the null and alternative hypotheses that, other factors being equal, the elasticity of rent with respect to \textit{pop} is different from zero.
(b) (5%) Test the null hypothesis stated in (a) at the 10% level.
(c) (5%) Test the null hypothesis stated in (a) at the 5% level.
(d) (5%) Find the 95% confidence interval associated with the null hypothesis stated in (a).

$3. Let rent be the average monthly rent, pop the total city population, avginc the average city income, and pctstu the student population as a percentage of the total population. One model to test for a relationship is ln(rent) = β0 + β1 ln(pop) + β2 ln(avginc) + β3 pctstu + u and the estimated equation is ln(rent) = 0.043 + 0.066 ln(pop) + 0.507 ln(avginc) + 0.006 pctstu (0.844) (0.039) (0.081) (0.002) n = 64 R^2 = 0.458 (a) (10%) State the null and alternative hypotheses that, other factors being equal, the elasticity of rent with respect to \textit{pop} is different from zero. (b) (5%) Test the null hypothesis stated in (a) at the 10% level. (c) (5%) Test the null hypothesis stated in (a) at the 5% level. (d) (5%) Find the 95% confidence interval associated with the null hypothesis stated in (a).$

Added by Matthew M.

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