## Introductory Econometrics

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This assignment is worth 20% of your ECON241 final mark.
Ø Unless it is specifically mentioned in the question, DO NOT copy and paste any Gretl output.

Ø Use Gretl to find critical values and p-values for all your test.
To save the data file: Right click on the data file and select ‘Save Link As.’ and save the
data file.
Note: Note: There will be a deduction of 20% of the total available marks for each 24
hour period or part thereof that the submission is late (for example, 25 hours late in
submission – 40% penalty).
Total marks: 50
The data file, House.gdt, contains data on house prices and various other determinants of
house prices. The variables are defined as follows:
price = house price, dollars.
sqmt = total living area in square metre (m2)
bdrms = number of bedrooms
age = age of house in years
traditional = 1 if traditional style; = 0 if other, such as townhouse, contemporary, etc.
small = 1 if (sqmt < 150; = 0 otherwise.
Medium = 1 if (sqmt ≥150 and sqmt <300); 0 otherwise.
Large = 1 if (sqmt > 300); 0 otherwise.
(Your answers to the questions regarding hypothesis testing should include all the
following steps: The null and alternative hypotheses, test statistic, the distribution of
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the test statistic under the null including the degrees of freedom, critical value(s),
decision rule and your conclusion. Follow and show all the hypothesis test steps
described in Chapter 3.4 in the textbook HGL, 4e. Use the critical value method to
make a decision. Assume that the random errors in the regression models are normally
distributed.)
Restrict your sample only for small houses for Q1-Q4 : (To restrict sample in Gretl
à select “sample” à “Restrict, based on criterion” à check box “Use dummy
variable” à then choose “small” from the dummy variable list. Note that there are
275 small houses in our sample. Gretl would show you the sample size as 1-275 after
you have restricted.)

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 à select “sample” à”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.)
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? = 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 theunrestricted 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?

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