The first data set (demand for housing) is used to apply the hedonic approach to
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The first data set (demand for housing) is used to apply the hedonic approach to demand estimation, while the second data set (demand for cigarettes) is used to apply the classical approach. Finally, the third dataset (cost of electricity) uses a well known dataset to estimate the cost of electricity production. In all cases the data is cross-sectional data. The estimation of demand follows two approaches: • the classical approach, whereby the quantity demanded of a product is explained by its own price, the prices of related goods (complements and substitutes), income, tastes and preferences, and the size of the population, among others; • the hedonic approach, whereby the price of an asset (car, house) is explained by the characteristics of the asset itself (i.e., the price of housing depends on the number of bedrooms, the number of bathroom, the view from the house (using a dummy variable: 1 = view, 0 = no view), the square footage of the house, the square footage of the lot, etc). PART 2: Assignment You are given the data on housing. The data are collected from the real estate pages of theBoston Globe during 1990. These are homes that sold in the Boston, MA area. The source of the data is Wooldridge (2009) Introductory Econometrics: A Modern Approach, 4th Edition, Cengage
Please keep in mind that when you interpret a regression coefficient, you are assuming that all the other variables remain constant. A Note on ANOVA The ANOVA table is used to test the null hypothesis that all regression coefficients (excluding the intercept term) are equal to zero against the alternative hypothesis that at least one is different from zero. This test is known as the F test for regression. The F test is computed as follows, under the assumption that the null hypothesis is true: The F statistics has two sets of degrees of freedom: numerator (attached to the Regression SS) and denominator degrees of freedom (attached to Residual SS). Excel computes the F statistic for you in the ANOVA table, and computes in the last column the level of significance (p-value). If the level of significance of the test is less than 5%, you will reject at the 5% level the null hypothesis that all regression parameters are zero. On the other hand, if the level of significance is greater than 5%, you will accept (i.e., fail to reject) the null hypothesis that all regression parameters are zero.
PRICE SQRFT ASSESS BDRMS LOTSIZE 300 2438 349.1 4 6126 370 2076 351.5 3 9903 191 1374 217.7 3 5200 195 1448 231.8 3 4600 373 2514 319.1 4 6095 466 2754 414.5 5 8566 332 2067 367.8 3 9000 315 1731 300.2 3 6210 206 1767 236.1 3 6000 240 1890 256.3 3 2892 285 2336 314 4 6000 300 2634 416.5 5 7047 405 3375 434 3 12237 212 1899 279.3 3 6460 265 2312 287.5 3 6519 227 1760 232.9 4 3597 240 2000 303.8 4 5922 285 1774 305.6 3 7123 268 1376 266.7 3 5642 310 1835 326 4 8602 266 2048 294.3 3 5494 270 2124 318.8 3 7800 225 1768 294.2 3 6003 150 1732 208 4 5218 247 1440 239.7 3 9425 275 1932 294.1 3 6114 230 1932 267.4 3 6710 343 2106 359.9 3 8577 477 3529 478.1 7 8400 350 2051 355.3 4 9773 230 1573 217.8 4 4806 335 2829 385 4 15086 251 1630 224.3 3 5763 235 1840 251.9 4 6383 361 2066 354.9 4 9000 190 1702 212.5 4 3500 360 2750 452.4 4 10892 575 3880 518.1 5 15634 209 1854 289.4 4 6400 225 1421 268.1 2 8880 246 1662 278.5 3 6314 713 3331 655.4 5 28231 248 1656 273.3 4 7050 230 1171 212.1 3 5305 375 2293 354 5 6637 265 1764 252.1 3 7834 313 2768 324 3 1000 417 3733 475.5 4 8112 253 1536 256.8 3 5850 315 1638 279.2 4 6660 264 1972 313.9 3 6637 255 1478 279.8 2 15267 210 1408 198.7 3 5146 180 1812 221.5 3 6017 250 1722 268.4 3 8410 250 1780 282.3 4 5625 209 1674 230.7 4 5600 258 1850 287 4 6525 289 1925 298.7 3 6060 316 2343 314.6 4 5539 225 1567 291 3 7566 266 1664 286.4 4 5484 310 1386 253.6 6 5348 471 2617 482 5 15834 335 2321 384.3 4 8022 495 2638 543.6 4 11966 279 1915 336.5 4 8460 380 2589 515.1 4 15105 325 2709 437 4 10859 220 1587 263.4 3 6300 215 1694 300.4 3 11554 240 1536 250.7 3 6000 725 3662 708.6 5 31000 230 1736 276.3 3 4054 306 2205 388.6 2 20700 425 1502 252.5 3 5525 318 1696 295.2 4 92681 330 2186 359.5 3 8178 246 1928 276.2 4 5944 225 1294 249.8 3 18838 111 1535 202.4 4 4315 268 1980 254 3 5167 244 2090 306.8 4 7893 295 1837 318.3 3 6056 236 1715 259.4 3 5828 202 1574 258.1 3 6341 219 1185 232 2 6362 242 1774 252 4 4950Explanation / Answer
Here the price of the house is the dependent variable and all other factors that influence the price of the house are the independent or explanatory variables. So, we could write the relation in functional form as follows--
Now, we could run the data on STATA and regress PRICE based on the explanatoy variables to get the result as follows--
. reg Price SQRFT ASSESS BDRMS LOTSIZE
Source | SS df MS Number of obs = 87
-------------+------------------------------ F( 4, 82) = 98.99
Model | 755214.063 4 188803.516 Prob > F = 0.0000
Residual | 156391.592 82 1907.21454 R-squared = 0.8284
-------------+------------------------------ Adj R-squared = 0.8201
Total | 911605.655 86 10600.0658 Root MSE = 43.672
------------------------------------------------------------------------------
Price | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
SQRFT | -.0008934 .0171889 -0.05 0.959 -.0350875 .0333007
ASSESS | .9092817 .1045863 8.69 0.000 .7012263 1.117337
BDRMS | 11.47135 6.585873 1.74 0.085 -1.630049 24.57275
LOTSIZE | .0005829 .0004988 1.17 0.246 -.0004095 .0015752
_cons | -37.77444 21.71907 -1.74 0.086 -80.98058 5.4317
------------------------------------------------------------------------------
Therefore, from the result above we could see that for all the variables except for ASSESS the result shows insignificant result. This we could see from the p-values, as lower the p-values, higher is the level of significance of not rejecting the null hypothesis whn it is true.
So, for 1% change in the ASSESS, the PRICE of house changes by 90%, which is explained by the coefficient of this explanatory variable.
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