252y0582h 12/5/05ECO252 QBA2Final EXAMDecember 14-16, 2005TAKE 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 isMIM = 2736 + 180 PMHSPredictor Coef SE Coef T PConstant 2736 2174 1.26 0.214PMHS 180.08 31.31 5.75 0.000S = 1430.91 R-Sq = 40.3% R-Sq(adj) = 39.1%Analysis of VarianceSource DF SS MS F PRegression 1 67720854 67720854 33.07 0.000Residual Error 49 100328329 2047517Total 50 168049183Unusual ObservationsObs 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 2.99RR 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 isMIM = - 1294 + 198 PMHS + 49.4 PURBAN - 42 MAGE + 247 NE + 757 MW + 1269 SO1252y0582h 12/5/05Predictor Coef SE Coef T P VIFConstant -1294 5394 -0.24 0.811PMHS 198.13 53.97 3.67 0.001 3.8PURBAN 49.36 14.27 3.46 0.001 1.4MAGE -42.1 151.6 -0.28 0.783 1.5NE 246.6 723.7 0.34 0.735 2.4MW 756.7 608.2 1.24 0.220 2.1SO 1268.9 863.0 1.47 0.149 5.2S = 1271.71 R-Sq = 57.7% R-Sq(adj) = 51.9%Analysis of VarianceSource DF SS MS F PRegression 6 96890414 16148402 9.99 0.000Residual Error 44 71158768 1617245Total 50 168049183Source DF Seq SSPMHS 1 67720854PURBAN 1 23781889MAGE 1 281110NE 1 1416569MW 1 193443SO 1 3496549Unusual ObservationsObs PMHS MIM Fit SE Fit Residual St Resid 50 81.9 21552 16999 543 4553 3.96RR 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. (MedianAge 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-c8Stepwise Regression: MIM versus PMHS, PURBAN, MAGE, NE, MW, SO Alpha-to-Enter: 0.15 Alpha-to-Remove: 0.15Response is MIM on 6 predictors, with N = 51Step 1 2Constant 2736 2528PMHS 180 134T-Value 5.75 4.46P-Value 0.000 0.000PURBAN 50T-Value 3.86P-Value 0.000S 1431 1263R-Sq 40.30 54.45R-Sq(adj) 39.08 52.55Mallows C-p 15.0 2.3More? (Yes, No, Subcommand, or Help)SUBC> yNo variables entered or removedMore? (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 2252y0582h 12/5/05any 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 2x variable too.
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