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Author: Amos Gilat
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![## Analysis of Home Prices and Market Returns
### Home Price Survey in a Metropolitan Area
A study of 40 home prices in a metropolitan area yielded the following results:
| Price | Less than $200,000 | Equal to $200,000 | More than $200,000 |
|---------------------|--------------------|-------------------|--------------------|
| Number of homes | 13 | 1 | 27 |
### Hypothesis Testing
1. **Hypothesis 1:**
- Test if the median price in the metropolitan area is $200,000.
2. **Hypothesis 2:**
- Test if the median price in the metropolitan area is more than $200,000.
Both tests use a significance level of α = 0.05. Formulate your hypotheses, apply the binomial approach, and detail your calculations, including p-values for both hypotheses.
### Regression Analysis on Market Returns
A proposed relationship between annual security return and market return can be defined by the regression model:
\[ y = mx + b + \varepsilon \]
- **y**: Annual return of the security
- **x**: Annual return of the market
- **b**: Intercept
- **ε**: Normally distributed noise
**Return** is calculated as:
\[ \text{Return} = \text{value at end of the year} + \text{received dividends during the year} - \text{value at the beginning of the year} \]
### Model Testing Approach
1. Retrieve annual data for a security of your choice and a financial index like the S&P 500 as the market indicator.
2. Use the past 20 years as your timeframe for analysis.
3. Conduct a regression analysis that includes hypothesis testing.
4. Report findings, include conclusions, significance levels, and present the final regression model.
5. Provide a scatterplot with the regression line, analyze residuals, and check their normality.
Consider if the model is valid. Determine whether there is a positive or adverse influence and specify if your regression model shows outperformance or underperformance relative to the market. Provide a detailed explanation of your work.](https://content.bartleby.com/qna-images/question/c75a416e-7821-4c4b-a434-6da28bc582d4/0cb34e92-d40e-4efa-9b70-5bcf5dd11b67/0off3v_processed.png)
Transcribed Image Text:## Analysis of Home Prices and Market Returns
### Home Price Survey in a Metropolitan Area
A study of 40 home prices in a metropolitan area yielded the following results:
| Price | Less than $200,000 | Equal to $200,000 | More than $200,000 |
|---------------------|--------------------|-------------------|--------------------|
| Number of homes | 13 | 1 | 27 |
### Hypothesis Testing
1. **Hypothesis 1:**
- Test if the median price in the metropolitan area is $200,000.
2. **Hypothesis 2:**
- Test if the median price in the metropolitan area is more than $200,000.
Both tests use a significance level of α = 0.05. Formulate your hypotheses, apply the binomial approach, and detail your calculations, including p-values for both hypotheses.
### Regression Analysis on Market Returns
A proposed relationship between annual security return and market return can be defined by the regression model:
\[ y = mx + b + \varepsilon \]
- **y**: Annual return of the security
- **x**: Annual return of the market
- **b**: Intercept
- **ε**: Normally distributed noise
**Return** is calculated as:
\[ \text{Return} = \text{value at end of the year} + \text{received dividends during the year} - \text{value at the beginning of the year} \]
### Model Testing Approach
1. Retrieve annual data for a security of your choice and a financial index like the S&P 500 as the market indicator.
2. Use the past 20 years as your timeframe for analysis.
3. Conduct a regression analysis that includes hypothesis testing.
4. Report findings, include conclusions, significance levels, and present the final regression model.
5. Provide a scatterplot with the regression line, analyze residuals, and check their normality.
Consider if the model is valid. Determine whether there is a positive or adverse influence and specify if your regression model shows outperformance or underperformance relative to the market. Provide a detailed explanation of your work.
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