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:

Weighted-Average Method

An inventory costing method that averages the costs of all similar items in inventory and assigns this average cost to the cost of units sold and to remaining inventory.

Canned Vegetable Soup

A processed food item made by combining vegetables and other ingredients, which are then sealed in cans and sterilized for preservation.

Mixing Department

A section within a manufacturing facility where raw materials are combined to form a product, particularly in industries like food, chemicals, and pharmaceuticals.

Bottling Department

A specialized unit within a manufacturing facility where products, typically liquids, are put into bottles for distribution.