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A Random Sample of 76 Apartments Is Collected near a University

question 294

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 $= 62.0 \% \quad$ R squared (adjusted) $= 61.5 \%$
$\mathrm { s } = 364.4$ with $76 - 2 = 74$ degrees of freedom

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

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Definitions:

Distilled Water

Water that has been boiled into vapor and condensed back into liquid, removing impurities and minerals.

Mitochondria

Membrane-bound organelles found in the cytoplasm of almost all eukaryotic cells, essential for producing energy via the process of oxidative phosphorylation.

Active Transport

The movement of molecules across a cell membrane from a region of lower concentration to one of higher concentration, requiring energy.

Facilitated Transport

A process of passive transport, mediated by carrier proteins, that allows substances to move across cell membranes without expending energy.