Please use Stata to replicate Ch9 Example 9.2 on pp.297-298.

Below is model (9.4):

price=β0+β1lotsize+β2sqrft+β3bdrms+u

Based on your estimation for model (9.4), answer the following questions:

(1) What is the null hypothesis of RESET test?

(2) What is the p-value for the RESET statistic?

(3) Do you reject the null hypothesis at the 5% significance level?

(4) Is there evidence of functional form misspecification in (9.4)?

Question

Please use Stata to replicate Ch9 Example 9.2 on pp.297-298.

Below is model (9.4):

price=β0+β1lotsize+β2sqrft+β3bdrms+u

Based on your estimation for model (9.4), answer the following questions:

(1) What is the null hypothesis of RESET test?

(2) What is the p-value for the RESET statistic?

(3) Do you reject the null hypothesis at the 5% significance level?

(4) Is there evidence of functional form misspecification in (9.4)?

BlackTom AI · Accepted Answer

We start by carefully unpacking the given question and the associated provided answer.

First, the question asks about several components of a RESET test for model (9.4): the null hypothesis, the p-value for the RESET statistic, the decision at the 5% level, and whether there is evidence of functional form misspecification.

Option (as provided in the answer):
- The null hypothesis is that model (9.4) on p.297 is correctly specified.
- p-value for the RESET statistic is 0.0120.
- Reject the null hypothesis at the 5% significance level.
- There is evidence of functional form misspecification in (9.4).

Analysis of each component:

1) Null hypothesis of RESET test:
- The RESET (Ramsey) test is designed to detect general misspecification in the functional form of a regression model. The null hypothesis posits that the specified model is correctly specified (no functional form misspecification). In practical terms, it means that the linear specification with the chosen regressors and any included powers or interactions used in the test does not omit important nonlinear relationships.
- The claim in the answer that the null is that model (9.4) is correctly specified aligns with the standard interpretation of RESET: the model is correctly specified under the null.

2) p-value for the RESET statistic:
- A p-value of 0.0120 indicates the probability, under the null hypothesis, of observing a RESET statistic as extreme or more extreme than the one computed from the data.
- Since 0.0120 is well below common significance levels (e.g., 0.05, 0.01), this low p-value provides evidence against the null of correct specification, suggesting possible misspecification.

3) Decision at the 5% significance level:
- At the 5% level (alpha = 0.05), we reject the null hypothesis if the p-value is less than 0.05.
- With a p-value of 0.0120, we would reject the null at the 5% level, concluding that there is evidence against correct specification in favor of misspecification.

4) Evidence of functional form misspecification in (9.4):
- Given the rejection of the null at 5%, the conclusion suggested by the RESET test is that there is evidence of functional form misspecification in model (9.4).
- This means the current specification may be missing nonlinear terms, interactions, or other structural features that would better capture the underlying relationship.

Putting these parts together, the statements in the provided answer correctly reflect the standard interpretation of a RESET test result in this context, assuming the reported p-value and the model setup are accurate. The reasoning for each component follows logically from the purpose of the RESET test and the conventional decision rule at the 5% level.

AS.440.606.50.SP25 M10: Assignment

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