Reconsider Example 6.16 in the text. In that example a number of models were assessed on their within-sample and out-of-sample predictive ability using data in the file \(b r 5\). Of the models considered, the one with the best within-sample performance, as judged by the \(\bar{R}^{2}\), AIC and SC criteria was

In this exercise we investigate whether we can improve on this function by adding the number of bathrooms (BATHS) and the number of bedrooms (BEDROOMS). Estimate the equations required to fill in the following table. The models have been numbered from 9 to 12 as extensions of those in Table 6.3. Model 2 is the same as equation (XR6.17). For the subsequent models extra variables are added, with model 12 being the last one considered. For the RMSE values, use the last 100 observations as the hold-out sample. Discuss the results. Include in your discussion a comparison with the results in Table 6.3.

Data From Example 6.16:-

Real estate agents and potential homebuyers are interested in valuing houses or predicting the price of a house with particular characteristics. There are many factors that have a bearing on the price of a house, but for our predictive model we will consider just two, the age of the house in years (AGE), and its size in hundreds of square feet (SQFT). The most general model we consider is

where PRICE is the house price in thousands of dollars. Of interest is whether some or all of the quadratic terms \(A G E^{2}\), \(S Q F T^{2}\), and \(A G E \times S Q F T\) improve the predictive ability of the model. For convenience, we evaluate predictive ability in terms of \(\ln (\) PRICE) not PRICE. We use data on 900 houses sold in Baton Rouge, Louisiana in 2005, stored in the data file br5. For a comparison based on the RMSE of predictions (but not the other criteria) we randomly chose 800 observations for estimation and 100 observations for the hold-out sample. After this random selection, the observations were ordered so that the first 800 were used for estimation and the last 100 for predictive assessment. Values of the criteria for the various models appear in Table 6.4. Looking for the model with the highest \(\bar{R}^{2}\), and the models with the smallest values (or largest negative numbers) for the AIC and SC, we find that all three criteria prefer model 2 where \(A G E^{2}\) is included, but \(S Q F T^{2}\) and \(A G E \times S Q F T\) are excluded. Using the out-of-sample RMSE criterion, model 6 , with \(A G E \times S Q F T\) included in addition to \(A G E^{2}\), is slightly favored over model 2.

Data From Table 6.3:-

Transcribed Image Text:

In(PRICE) = B + BAGE + 3SQFT + AGE + e (XR6.17)