A Random Sample of 76 Apartments Is Collected near a University

question 8

Essay

A random sample of 76 apartments is collected near a university. All of the apartments in
the sample have between 1 and 6 bedrooms. The variables recorded for each apartment are
Rent (in dollars) and the number of Bedrooms. The regression output is: The dependent variable is Rent
R squared $= 62.0 \% \quad \mathrm { R }$ squared (adjusted) $= 61.5 \%$ $s = 364.4$ with $76 - 2 = 74$ degrees of freedom
\begin{tabular} { l c c r r }
\multicolumn{1}{c} { Variable } & Coeff & SE(Coeff) & t-ratio & p-value \\
Constant & $357.795$ & $111.6$ & $3.2$ & $0.0020$ \\
Bedrooms & $400.554$ & $36.42$ & $11.0$ & $< 0.0001$
\end{tabular}
a. Write out the regression equation.
b. Compute a 95% confidence interval for the coefficient of Bedrooms. Explain your
confidence interval in the context of the problem.
c. Based on your interval is the number of bedrooms a significant predictor of rent? Explain
how you reached your answer.
d. Explain the meaning of the regression intercept in the context of this problem.
e. Use the plots below to check the regression conditions.

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Definitions:

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A medical procedure used in prenatal diagnosis to extract a small amount of amniotic fluid for the testing of chromosomal abnormalities in a fetus.