闪电代写 -代写CS作业_CS代写_Finance代写_Economic代写_Statistics代写_代码代做_IT代写_加急帮助

Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

Introductory Econometrics

Econ 399

Spring 2022

Assignment 1

Question 1

Suppose a mortgage broker is interested in examining the relationship between the depreciation to a house price (Y), and the number of days a house has been in the market (X). To examine this relationship, we estimated the following basic statistics based on a sample of 10 houses:

Yi = 1800 Xi = 420 Yi2 = 417400 Xi(2) = 20964

Xi Yi = 92260 u i(2) = 9899.519 n=10

Use the above information to answer the following questions:

1. Compute the OLS estimates of the intercept coefficient β0 and the slope coefficient β1 .

2. Interpret the estimated coefficient p1.

3. What is the predicted value of Y when X=2

4. Calculate an estimate of the error variance G2.

5. Calculate an estimate of the standard error of the slope coefficient β1.

6. Compute the value of the coefficient of determination R2 . Briefly explain what the calculated value of R2 means.

Question 2

Consider the following simple regression model: y = p0 + u Assume that the classical assumptions about this model apply.

1) Derive the ordinary least squares (OLS) estimator of p0

2) Derive the expected value of the OLS estimator ! . Is ! an unbiased estimator of p0?Why?

Question 3

Briefly explain the following in words or equations as appropriate

1) Type 1 error

2) Level of significance

3) Degrees of freedom

4) Given = 4 and SE () = 2, test the null hypothesis that p = 0 (versus the alternative hypothesis that it does not equal zero) with 13 degrees of freedom at the 5% level of significance.

5) State the Gauss-Markov theorem, its conditions and briefly explain the properties of the estimator specified by it.

Question 4

Use the data set made available on eclass titled “HPRICE.txt" to answer this question. The sample contains data on 88 houses and includes the following variables:

Price: price of the house in dollars

bedrooms: number of bedrooms

lotsize: size of lot in square feet

sqrft: size of house in square feet

Colonial: a dummy variable, equals1 if the house has a colonial style and equals zero otherwise.

Enter the data into STATA and then answer the following questions:

1. Use OLS to estimate the following log-linear multiple regression equation where ln price is the natural logarithm of price.

ln price = β0 + β1lotsize + β2 sqrft + β3 bedrooms + β4 colonial + u

2. Interpret all the estimated coefficients.

3. Explain what the calculated value of the coefficient of determination R2 means.

4. Develop and test appropriate hypotheses about the individual slope coefficients β2 and β4 at the 5% significance level.

5. Construct a 95% confidence interval estimate of the true β 1 and β2 coefficients and interpret it.

6. Which of the four explanatory variables has more effect on the dependant variable? and why?

7. Suppose that all the Classical Assumptions hold. Does this mean that the estimated (marginal) effect of the sqrft on price is the true parameter? Why?

8. Develop and test an appropriate hypothesis about the overall fit of the model at the 5% significance level.

9. Based on the estimated model in number (1), test the exclusion restriction that both coefficients β2 and β3 are jointly equal to zero at the 5% significance level.

10. Suppose we change the unit of measurement of the dependant variable (price) and we express it in thousands rather than in dollars.

Generate a new variable pice2 = . Re-estimate the regression equation in part (1) using price2 as the new dependant variable. What do you realize has 2