A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Consider the monthly rent (Rent in $) of a home in Ann Arbor, Michigan, as a function of the number of bedrooms (Beds), the number of bathrooms (Baths), and square footage (Sqft).

[Image: Click here for the Excel Data File]

a. Estimate: \( \text{Rent} = \theta_0 + \theta_1 \text{Beds} + \theta_2 \text{Baths} + \theta_3 \text{Sqft} + \varepsilon \). (Round your answers to 2 decimal places.)

\[ \text{Rent} = \]
\[ + \text{Bed} + \]
\[ \text{Bath} + \]
\[ \text{Sqft} \]

b-1. Which of the predictor variables is most likely to be the cause of changing variability?
- Beds because it is likely correlated with Rent.
- Baths because its distribution tends to be highly skewed.
- Sqft because the variability of rent tends to increase with square footage.

b-2. Discuss the consequences of changing variability (heteroskedasticity).
- OLS estimators and their standard errors are both biased.
- OLS estimators are biased but their standard errors are unbiased.
- OLS estimators are unbiased but their standard errors are biased.
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Transcribed Image Text:Consider the monthly rent (Rent in $) of a home in Ann Arbor, Michigan, as a function of the number of bedrooms (Beds), the number of bathrooms (Baths), and square footage (Sqft). [Image: Click here for the Excel Data File] a. Estimate: \( \text{Rent} = \theta_0 + \theta_1 \text{Beds} + \theta_2 \text{Baths} + \theta_3 \text{Sqft} + \varepsilon \). (Round your answers to 2 decimal places.) \[ \text{Rent} = \] \[ + \text{Bed} + \] \[ \text{Bath} + \] \[ \text{Sqft} \] b-1. Which of the predictor variables is most likely to be the cause of changing variability? - Beds because it is likely correlated with Rent. - Baths because its distribution tends to be highly skewed. - Sqft because the variability of rent tends to increase with square footage. b-2. Discuss the consequences of changing variability (heteroskedasticity). - OLS estimators and their standard errors are both biased. - OLS estimators are biased but their standard errors are unbiased. - OLS estimators are unbiased but their standard errors are biased.
The table presents data on rental properties, detailing the rent cost alongside the number of bedrooms (Beds), bathrooms (Baths), and square footage (Sqft) for both one-section and two-section listings. Below is the data outlined in two columns:

### Column 1
- **Rent**: Monthly rent in dollars.
- **Beds**: Number of bedrooms.
- **Baths**: Number of bathrooms.
- **Sqft**: Square footage of the property.

### Column 2
- **Rent**: Monthly rent in dollars for different-sized properties.
- **Beds**: Number of bedrooms.
- **Baths**: Number of bathrooms.
- **Sqft**: Square footage of the property.

#### Detailed Data:

| Rent  | Beds | Baths | Sqft |
|-------|------|-------|------|
| 645   | 1    | 1     | 500  |
| 675   | 1    | 1     | 648  |
| 760   | 1    | 1     | 700  |
| 800   | 1    | 1     | 903  |
| 820   | 1    | 1     | 817  |
| 850   | 2    | 1     | 920  |
| 855   | 1    | 1     | 900  |
| 859   | 1    | 1     | 886  |
| 900   | 1    | 1.5   | 1000 |
| 905   | 2    | 1     | 920  |
| 905   | 2    | 1     | 876  |
| 929   | 2    | 1     | 920  |
| 960   | 2    | 1     | 975  |
| 975   | 2    | 2     | 1100 |
| 990   | 1    | 1.5   | 940  |
| 995   | 2    | 1     | 1000 |
| 1029  | 2    | 2     | 1299 |
| 1039  | 2    | 2     | 1164 |
| 1049  | 2    | 2     | 1180 |
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Transcribed Image Text:The table presents data on rental properties, detailing the rent cost alongside the number of bedrooms (Beds), bathrooms (Baths), and square footage (Sqft) for both one-section and two-section listings. Below is the data outlined in two columns: ### Column 1 - **Rent**: Monthly rent in dollars. - **Beds**: Number of bedrooms. - **Baths**: Number of bathrooms. - **Sqft**: Square footage of the property. ### Column 2 - **Rent**: Monthly rent in dollars for different-sized properties. - **Beds**: Number of bedrooms. - **Baths**: Number of bathrooms. - **Sqft**: Square footage of the property. #### Detailed Data: | Rent | Beds | Baths | Sqft | |-------|------|-------|------| | 645 | 1 | 1 | 500 | | 675 | 1 | 1 | 648 | | 760 | 1 | 1 | 700 | | 800 | 1 | 1 | 903 | | 820 | 1 | 1 | 817 | | 850 | 2 | 1 | 920 | | 855 | 1 | 1 | 900 | | 859 | 1 | 1 | 886 | | 900 | 1 | 1.5 | 1000 | | 905 | 2 | 1 | 920 | | 905 | 2 | 1 | 876 | | 929 | 2 | 1 | 920 | | 960 | 2 | 1 | 975 | | 975 | 2 | 2 | 1100 | | 990 | 1 | 1.5 | 940 | | 995 | 2 | 1 | 1000 | | 1029 | 2 | 2 | 1299 | | 1039 | 2 | 2 | 1164 | | 1049 | 2 | 2 | 1180 |
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