Econometrics Assignment

1. [5 marks] Obtain a scatter plot between house price (price) against total square metre (sqmt) and comment on your plot. Copy and paste your graph here. 

(To obtain a scatter plot in Gretl, → View → graph specified vars → XY Scatter →  X-axis variables (sqrft) →Y-axis variable (price) and ok.) 

2. [5 marks] Estimate the following linear regression model. 

������ = �� + ������� + ��. 

Is there significant evidence that an increase in the total living area by one square  meter increases the price of a small house by less than 500, on average? Test this at the  1% significance level and clearly state your conclusion. Copy and paste your regression output.  

3. [5 marks] A first home buyer is interested in a small house with the total living area of  100 square meters, but she is not sure if the asking price of $ 85,000 is not too high.  Test the null hypothesis that the asking price is the right price for a house of that size  against the alternative hypothesis that it is too high. Use the 5% significance level. 
4. [5 marks] Construct a 95% prediction interval for a small house with the living area of  100 square meters, and interpret the interval. 

Restore the full sample range and answer the followings. (To restore full sample  range in Gretl select 'sample' 'restore full range'.) 

5. [5 marks] Estimate the following regression model using all houses in the sample. Then, provide a summary report and discuss your summary report in terms of the  significance of each coefficient, R2 and overall significance of the model. (You are not  required to carry out full hypothesis testing for this question.) 

������ = �� + ������� + ������ + �������� + �� 

(Note: a summary report should contain the estimated regression equation, standard errors, t ratios, the number of observations, goodness of fit statistic, and the F value for  the overall significance test. See the example below.)

2 

� = 5.6 − 0.06�1 + 0.43�2 

�� . . ? . . . . ? . . . . ? . . 

� . . ? . . . . ? . . (. . ? . . ) 

� = ? �K = ? � = ? 

6. [5 marks] Compute and interpret the elasticity of price with respect to sqmt for a home  that is 250 square metres large, 15 years old, and has two bedrooms. 
7. [5 marks] Is there evidence to claim that the price of a house decreases by more than  1200 dollars for each year it becomes older? Use a hypothesis testing at 5% to answer  this question. Clearly state your conclusion. 
8. [5 marks] Based on the model in question 5, test if age and bdrms are jointly not  important in determining house prices at 5%. Clearly state the restricted and the  unrestricted models, the null and alternative hypotheses, the test statistic and it  distribution under the null, the critical values, and your conclusion. (Copy and paste  your Gretl output for the restricted model.)  
9. [5 marks] Estimate the following regression model and test the overall significance of  the model. Use the 5% significance level. Follow all the steps for hypothesis testing. 

��(������) = �� + ������� + ������ + �������� + ��������� + �� 

10. [5 marks] Compare the models in Q5 and Q9, and comment on the validity of each  model. Which model would you prefer and why?

Question 2

Figure 2: Linear Regression Analysis

Given,

= + + .

From figure 2, the regression equation will be:

= 29644.3 + 498.169 + 30196.01

Choice of Statistics

As population variance is not known and the sample size is large, t statistics is preferred in this case.

Framing a Hypothesis

Ho: dprice/dsqmt >= 500

H1: dprice/dsqmt  < 500