Economics

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- [5 marks] Obtain a scatter plot between house price (
) against total square metre (*price**sqm**t*) 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.) *

- [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**.

- [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.
- [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 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,
*R*2 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 = ? � = ?

- [5 marks] Compute and interpret the elasticity of
with respect to*price*for a home that is 250 square metres large, 15 years old, and has two bedrooms.*sqmt* - [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.
- [5 marks] Based on the model in question 5, test if
and*age*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.*bdrms***(Copy and paste your***Gretl***output for the restricted model.)** - [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.

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

- [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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**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