attachments_f0f4daaa43b84d0924d3723ea0badf1f1f48e5ec month date trips lowtemp weekend schoolvacation 1 1 3046 30 0 0 1 2 3368 33 0 0 1 3 1636 18 0 0 1 4 2275 17 1 0 1 5 2083 31 1 0 1 6 3565 11 0 0 1 7 2339 6 0 0 1 8 3973 13 0 0 1 9 4999 29 0 0 1 10 1863 28 0 0 1 11 1974 37 1 0 1 12 5483 36 1 0 1 13 6912 32 0 0 1 14 5133 41 0 0 1 15 6515 39 0 0 1 16 6075 34 0 0 1 17 6181 31 0 0 1 18 3361 25 1 0 1 19 4143 25 1 0 1 20 5376 38 0 1 1 21 1778 17 0 0 1 22 1466 9 0 0 1 23 2458 12 0 0 1 24 2656 11 0 0 1 25 2280 22 1 0 1 26 2598 19 1 0 1 27 4541 28 0 0 1 28 3166 13 0 0 1 29 3188 13 0 0 Page 1 Name (Last, First) _________________________________________ Email ID: ____________________@psu.edu ECON 306 Homework 5 Due: Tuesday, November 29, 2016 Instructions: Please print out and complete the following assignment writing your answers clearly and showing your work directly on the assignment. Please keep a log of your work in STATA and print out and attach all of your results. Use a highlighter to highlight all of your commands in STATA (this will make it easier for the graders to see your work). Follow directions carefully (underlining or circling where indicated in your STATA output). Be sure to turn the assignment in at the beginning of class on Tuesday, November 29. Late homeworks cannot be accepted. Capital Bike Share is a service provided in the Washington D.C. area that allows individuals to use bicycles for short-term use; individuals pick up the bike at \"Point A\" and then return it at \"Point B.\" Using data collected from this service, we want to look at the relationship between number of trips made per day and daily low temperature. This dataset comes from one single month (January) where the column \"date\" denotes each day of the month. a. Run the following regression in STATA: trips = 0 + 1*lowtemp b. Report the coefficient and p-value on lowtemp. Is this statistically significant? c. Using STATA, plot the residuals (attach to this assignment). What general conclusions might you draw from looking at this plot? d. Perform a Durbin-Watson test at the .05 level testing that there is positive serial correlation. Be sure to report the lower and upper limit critical values and test statistic. What is your decision, and what does this mean? Suppose we have the following data on the income and consumption of non-self-employed homeowners: (Data comes from Ando & Modigliani's \"The Permanent Income and Life Cycle Hypotheses of Saving Behavior: Comparisons and Tests\") Income Bracket ($) 0-999 1000-1999 2000-2999 3000-3999 4000-4999 5000-5999 6000-7499 7500-9999 10000-above Average Income ($) 556 1622 2664 3587 4535 5538 6585 8582 14033 Average Consumption ($) 2760 1930 2740 3515 4350 5320 6250 7460 11500 a. Run a regression to explain average consumption as a function of average income. Show your work in STATA and report your results below: Coefficient Std. Error t P > |t| Average income b. Use the Park test to test the residuals from the equation you ran in part a for heteroscedasticity, using average income as the potential proportionality factor Z (Use =.05). Report the coefficient and pvalue on the proportionality factor. What do you conclude as a result? c. Run a 5-percent White test to test for heteroscedasticity. Report the test statistic and critical value then provide your conclusion. d. Formulate the White test regression that is used. (Write this down here) Then, run the regression in STATA. Use the output to show how STATA calculates the White test statistic (write the numbers). e. In this example, the ranges of the income brackets are not constant, so the variables are means of ranges of differing widths. Therefore, it would seem reasonable to think that different range widths might produce different variances for the error term, making heteroscedasticity even more likely. Re-run the regression from part a using heteroskedastic-corrected standard errors. Report your results below: Coefficient Std. Error t P > |t| Average income You are looking at data on determinants of housing prices. An example dataset can be found in the Excel spreadsheet: House_price.xls: price = house price, $1000s lotsize = size of lot in square feet sqrft = size of house in square feet We want \"price\" to be our dependent variable and the other variables to be our independent variables; however, we believe that heteroskedasticity may be a concern because of the large range in housing prices. Why would taking the natural log of our variables (creating a double log form) be a possible solution to our problem? Explain. [Hint: If you are not sure, try taking the natural log of the price column to see how it changes the values] price lotsize sqrf 300 6126 370 9903 191 5200 195 4600 373 6095 466.275 8566 332.5 9000 315 6210 206 6000 240 2892 285 6000 300 7047 405 12237 212 6460 265 6519 227.4 3597 240 5922 285 7123 268 5642 310 8602 266 5494 270 7800 225 6003 150 5218 247 9425 275 6114 230 6710 343 8577 477.5 8400 350 9773 230 4806 335 15086 251 5763 235 6383 361 9000 190 3500 360 10892 575 15634 209.001 6400 225 8880 246 6314 713.5 28231 248 7050 230 5305 375 6637 265 7834 313 1000 2438 2076 1374 1448 2514 2754 2067 1731 1767 1890 2336 2634 3375 1899 2312 1760 2000 1774 1376 1835 2048 2124 1768 1732 1440 1932 1932 2106 3529 2051 1573 2829 1630 1840 2066 1702 2750 3880 1854 1421 1662 3331 1656 1171 2293 1764 2768 417.5 253 315 264 255 210 180 250 250 209 258 289 316 225 266 310 471.25 335 495 279.5 380 325 220 215 240 725 230 306 425 318 330 246 225 111 268.125 244 295 236 202.5 219 242 8112 5850 6660 6637 15267 5146 6017 8410 5625 5600 6525 6060 5539 7566 5484 5348 15834 8022 11966 8460 15105 10859 6300 11554 6000 31000 4054 20700 5525 92681 8178 5944 18838 4315 5167 7893 6056 5828 6341 6362 4950 3733 1536 1638 1972 1478 1408 1812 1722 1780 1674 1850 1925 2343 1567 1664 1386 2617 2321 2638 1915 2589 2709 1587 1694 1536 3662 1736 2205 1502 1696 2186 1928 1294 1535 1980 2090 1837 1715 1574 1185 1774