252y0582h 12 5 05 ECO252 QBA2 Final EXAM December 14 16 2005 TAKE HOME SECTION Name Student Number Class days and time III Take home Exam 20 points A 4th computer problem 5 This is an internet project You should do only one of the following 2 problems Problem 1 In his book Statistics for Economists An Intuitive Approach New York HarperCollins 1992 Alan S Caniglia presents data for 50 states and the District of Columbia These data are presented as an appendix at the end of this section The Data Consists of six variables The dependent variable MIM the mean income of males having income who are 18 years of age or older PMHS the percent of males 18 and older who are high school graduates PURBAN the percent of total population living in an urban area MAGE the median age of males Using his data I got the results below Regression Analysis MIM versus PMHS The regression equation is MIM 2736 180 PMHS Predictor Constant PMHS S 1430 91 Coef 2736 180 08 SE Coef 2174 31 31 T 1 26 5 75 R Sq 40 3 P 0 214 0 000 Analysis of Variance Source DF SS Regression 1 67720854 Residual Error 49 100328329 Total 50 168049183 R Sq adj 39 1 MS 67720854 2047517 F 33 07 P 0 000 Unusual Observations Obs PMHS MIM Fit SE Fit Residual St Resid 1 69 1 12112 15180 200 3068 2 17R 3 71 6 12711 15630 215 2919 2 06R 50 81 9 21552 17485 447 4067 2 99R R denotes an observation with a large standardized residual His only comment is that a 1 increase in the percent of males that are college graduates results is associated with about a 180 increase in male income and that there is evidence here that the relationship is significant He then describes three dummy variables NE 1 if the state is in the Northeast Maine through Pennsylvania in his listing MW 1 if the state is in the Midwest Ohio through Kansas and SO 1 if the state is in the South Delaware through Texas If all of the dummy variables are zero the state is in the West Montana through Hawaii I ran the regression with all six independent variables To check these variables look at his data MTB regress c2 6 c3 c8 SUBC VIF SUBC brief 2 Regression Analysis MIM versus PMHS PURBAN MAGE NE MW SO The regression equation is MIM 1294 198 PMHS 49 4 PURBAN 42 MAGE 247 NE 757 MW 1269 SO 1 252y0582h 12 5 05 Predictor Constant PMHS PURBAN MAGE NE MW SO S 1271 71 Coef 1294 198 13 49 36 42 1 246 6 756 7 1268 9 SE Coef 5394 53 97 14 27 151 6 723 7 608 2 863 0 T 0 24 3 67 3 46 0 28 0 34 1 24 1 47 R Sq 57 7 DF 1 1 1 1 1 1 VIF 3 8 1 4 1 5 2 4 2 1 5 2 R Sq adj 51 9 Analysis of Variance Source DF SS Regression 6 96890414 Residual Error 44 71158768 Total 50 168049183 Source PMHS PURBAN MAGE NE MW SO P 0 811 0 001 0 001 0 783 0 735 0 220 0 149 MS 16148402 1617245 F 9 99 P 0 000 Seq SS 67720854 23781889 281110 1416569 193443 3496549 Unusual Observations Obs PMHS MIM Fit SE Fit Residual St Resid 50 81 9 21552 16999 543 4553 3 96R R denotes an observation with a large standardized residual He has asked whether region affects the independent variable on the strength of the significance tests in the output above he concludes that the regional variables do not have any affect on male income Median Age looks pretty bad too There are two ways to confirm these conclusions Caniglia does one of these an F test that shows whether the regional variables as a group have any effect He says that they do not Another way to test this is by using a stepwise regression MTB stepwise c2 c3 c8 Stepwise Regression MIM versus PMHS PURBAN MAGE NE MW SO Alpha to Enter 0 15 Alpha to Remove 0 15 Response is MIM on 6 predictors with N 51 Step Constant PMHS T Value P Value 1 2736 2 2528 180 5 75 0 000 134 4 46 0 000 PURBAN T Value P Value S R Sq R Sq adj Mallows C p 50 3 86 0 000 1431 40 30 39 08 15 0 1263 54 45 52 55 2 3 More Yes No Subcommand or Help SUBC y No variables entered or removed More Yes No Subcommand or Help SUBC n What happens is that the computer picks PMHS as the most valuable independent variable and gets the same result that appeared in the simple regression above It then adds PURBAN and gets MIM 2528 134 PMHS 50 PURBAN The coefficients of the 2 independent variables are significant the adjusted R Sq is higher than the adjusted R sq with all 6 predictors and the computer refuses to add 2 252y0582h 12 5 05 any more independent variables So it looks like we have found our best regression See the text for interpretation VIFs and C p s So here is your job Update this work Use any income per person variable a mean or a median for men women or everybody Find measures of urbanization or median age Fix the categorization of states if you don t like it Regress state incomes against the revised data Remove the variables with insignificant coefficients If you can think of new variables add them Last year I suggested trying percent of output or labor force in manufacturing Make sure that you pick variables that can be compared state to state Though you can legitimately ask whether size of a state affects per capita income using total amount produced in manufacturing is poor because it s just going to be big for big states Similarly the fraction of the workforce with a certain education level is far better then the number For instructions on how to do a regression try the material in Doing a Regression For data sources try the sites mentioned in 252Datalinks Use F tests for adding the regional variables and use stepwise regression Don t give me anything you don t understand Problem 2 Recently the Heritage Foundation produced the graph below What I want to know is if you can develop an equation relating per capita income the dependent variable and Economic freedom x Because it is pretty obvious that a straight line won t work you will probably need to create a x 2 variable too But I would like to know what parts of economic freedom affect per capita income In addition to the Heritage Foundation Sources the CIFP site mentioned in 252datalinks and the CIA Factbook might provide some interesting independent variables You should probably use a sample of no more than 50 countries and it s up to you what variables to use You are of course looking …
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