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# ps1_sol - SOLUTIONS TO Problem Set 1 Introduction to...

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SOLUTIONS TO Problem Set 1 Introduction to Econometrics prepared by Prof. Marcelo J. Moreira and Seyhan E Arkonac, PhD for all sections Spring 2010 “Calculator” was once a job description. This problem set gives you an opportunity to do some calculations on the relation between smoking and lung cancer, using a (very) small sample of five countries. The purpose of this exercise is to illustrate the mechanics of ordinary least squares (OLS) regression. First you will calculate the regression “by hand” using formulas from class and the textbook, then you will use STATA to confirm the calculation. For the “by hand” calculations, you may relive history and use long multiplication, long division, and tables of square roots and logarithms; or you may use an electronic calculator or a spreadsheet. The data are summarized in the following table. The variables are per capita cigarette consumption in 1930 (the independent variable, “ X ”) and the death rate from lung cancer in 1950 (the dependent variable, “ Y ”). The cancer rates are shown for a later time period because it takes time for lung cancer to develop and be diagnosed. Observation # Country Cigarettes consumed per capita in 1930 ( X ) Lung cancer deaths per million people in 1950 ( Y ) 1 Switzerland 530 250 2 Finland 1115 350 3 Great Britain 1145 465 4 Canada 510 150 5 Denmark 380 165 Source: Edward R. Tufte, Data Analysis for Politics and Management , Table 3.3. 1. Use a calculator, a spreadsheet, or “by hand” methods to compute the following; refer to the textbook for the necessary formulas. ( Note : if you use a spreadsheet, attach a printout) a) The sample means of X and Y , X and Y . b) The standard deviations of X and Y , s X and s Y . c) The correlation coefficient, r , between X and Y d) 1 ˆ , the OLS estimated slope coefficient from the regression Y i = 0 + 1 X i + u i e) 0 ˆ , the OLS estimated intercept term from the same regression f) ˆ i Y , i = 1,…, n , the predicted values for each country from the regression g) ˆ i u , the OLS residual for each country.

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Answers: a) The sample means of X and Y , X and Y . X = 736, Y = 276 b) The standard deviations of X and Y , s X and s Y . s X = 364.41, s Y = 132.35 c) The correlation coefficient, r , between X and Y r = 0.9262 d) 1 ˆ , the OLS estimated slope coefficient from the regression Y i = 0 + 1 X i + u i 1 ˆ = 0.336418 e) 0 ˆ , the OLS estimated intercept term from the same regression 0 ˆ = 28.39656 f) ˆ i Y , i = 1,…, n , the predicted values for each country from the regression Switzerland 206.6981 France 403.5026 GreatBritain 413.5952 Canada 199.9697 Denmark 156.2354 g) ˆ i u , the OLS residual for each country. Switzerland 43.3019 France -53.5026 GreatBritain 51.40483 Canada -49.9697 Denmark 8.7646 2. Now calculate the statistics in question #1 using STATA. On the STATA output file, find and label the items in Question #1. STATA HINTS: First load STATA and type “edit,” which brings up something that looks like a spreadsheet. Enter the smoking and cancer values in the first two columns. Double- click the column headers to enter variable names (e.g. “smoke”, “deaths”). Close the editor window when you are done. The following commands will be useful: list
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ps1_sol - SOLUTIONS TO Problem Set 1 Introduction to...

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