You will need to use the HW2 dataset to answer the following questions. This data set contains data on houses sold in Denver County, CO during mid-2006. The data set includes sale price, the house size in square feet, its age and a variable for whether it has a pool, or fireplace or if it is on the waterfront.

Variable Description

price sale price, dollars

sqft total square feet

bedrooms number of bedrooms

baths number of full baths

age age in years

Owner \(\quad=1\) if owner occupied at sale;

\(=0\) if vacant or tenant

Pool \(=1\) if pool present

\(=0\) otherwise

Traditional \(=1\) if traditional style;

\(=0\) otherwise, such as townhouse, contemporary, etc.

Fireplace \(\quad=1\) if fireplace present

\(=0\) otherwise

Waterfront \(=1\) if on waterfront

\(=0\) otherwise

You will need to use the EXCEL spreadsheet/output to answer the following questions.

In this assignment, you have estimated the parameters of the following equations using

OLS:

Case 1:

\(\text { PRICE } E_{i}=B_{1}+B_{2} S Q F T_{i}+B_{3} A G E_{i}+B_{4} \text { Baths }+B_{5} \text { Bedrooms }+e_{i}\)

1. Report you results of the estimated regression in the form of an equation. Write your results listing the standard errors in parentheses under the numerical estimates of each estimator.
2. Explain the economic meaning of each of the estimated coefficients, excluding the coefficient of the constant term.
3. What is your forecast of the average housing price with the mean value of each of the independent variables?
4. What are the values of \(R^{2}\) and \(\bar{R}^{2}\) in this example? What is the economic meaning of \(\bar{R}^{2}\) in this example? Why do we use \(\bar{R}^{2}\) instead of \(R^{2}\) ?
5. Test the hypothesis that whether age of the house has an impact on the housing price at the \(5 \%\) level. Be sure to state: the null and alternative hypothesis, the critical value of the test statistic, the computed value of the test statistic, the criterion for acceptance or rejection of the null hypothesis, and your conclusion. [Hint: 5 steps for hypothesis]
6. Test the hypothesis that none of the independent variables (excluding the constant term) is statistically significant at the \(5 \%\) level.
7. Test the hypothesis that whether the number of Bedrooms and the number of the bathrooms are jointly not significantly different from zero at the $5 \%$ significance level. Be sure to state: the null and alternative hypothesis, the critical value of the test statistic, the computed value of the test statistic, the criterion for acceptance or rejection of the null hypothesis, and your conclusion. [Hint: 5 steps for hypothesis]
   Case 2:
   Estimate the following model:
   
8. Write your estimate in equation form, listing the standard errors, t-value, and P-value in parentheses under the numerical estimates of each estimator. Using stars to indicate \(5 \%\) significance levels, and listing the \(R^{2}\) and \(\bar{R}^{2}\).
9. What variables are dummy variable in this model?
10. How do you interpret the dummies in this model?
11. Which of the dummies are statistically significant?
12. There is a famous economist, Dr. Dolaamo, suggests you to include SQFT square in your model. So, you have to create a variable that is SQFT square, call $S Q F T 2$, and estimate again your new model, Model $B$. What is the rationale for the introduction of SQFT and SQFT2 as explanatory variable? Do the observed signs of these variables make economic sense?
    Model B
    \(\begin{aligned}
    \ln \left(\text { PRICE }_{i}\right)=& B_{1}+B_{2} S Q F T_{i}+B_{3}\left(S Q F T 2_{i}\right)+B_{4}\left(\text { Bedrooms }_{i}\right)+B_{5}\left(\text { Baths }_{i}\right)+B_{6}\left(\text { Age }_{i}\right)+B_{7}\left(\text { Owner }_{i}\right) \\
    &+B_{8}\left(\text { Pool }_{1}\right)+B_{9}\left(\text { Tradiational }_{i}\right)+B_{10}\left(\text { Firplace }_{i}\right)+B_{11}\left(\text { Waterfront }_{i}\right)+e_{i}
    \end{aligned}\)
13. Now, there is another professor, Dr. Santa, thinks you have to include another new variable WT, which is the product of Waterfront and Traditional. So, you have to create a variable that is WT, and re-estimate again your new model, Model C. What is the effect, t-value and \(\bar{R}^{2}\), of adding this variable? Interpret the of this interaction variable, and discuss its sign and statistical significance.
    Model C
    \(\begin{aligned}
    \ln \left(\text { PRICE }_{i}\right)=& B_{1}+B_{2} \operatorname{SQF} T_{i}+B_{3}\left(\text { SQFT }_{i}\right)+B_{4}\left(\text { Bedrooms }_{i}\right)+B_{5}\left(\text { Baths }_{i}\right)+B_{6}\left(\text { Age }_{i}\right)+B_{7}\left(\text { Owner }_{i}\right) \\
    &+B_{8}\left(\text { Pool }_{1}\right)+B_{9}\left(\text { Tradiational }_{i}\right)+B_{10}\left(\text { Firplace }_{i}\right)+B_{11}\left(\text { Waterfront }_{i}\right)+B_{12}(\text { WT })+e_{i}
    \end{aligned}\)
14. Using Model C predict the value of a traditional style house with 2500 square feet of area, that is 20 years old, which is owner occupied, with fireplace, but no pools with 4 bedrooms, 3 bathrooms, and not on the waterfront.

Price: $26.82

Solution: The downloadable solution consists of 14 pages, 1282 words and 1 charts.
Deliverable: Word Document