EconRegressionAnalysis

- Regression Analysis Introduction to Statistics STAT 210 Spring Quarter 2008 1 So what is this all about Lets assume we want to investigate the

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1 Regression Analysis Introduction to Statistics STAT 210 Spring Quarter 2008
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2 So what is this all about??? Let’s assume we want to investigate the following relationships What is the relationship between student performance and class size? What is the relationship between education and wages? Do I earn more if I drink a lot? No really !
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3 600 620 640 660 680 700 15 20 25 Test Scores and Student-Teacher Ratio Student-Teacher Ratio Test Scores
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4 0 10 20 30 40 50 5 10 16 20 Highest Grade Attended Hourly Earning and Education Earnings per hour 12
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5 Introduction Let’s look at the two examples Student Test Scores and Student-Teacher Ration Wages and Education Both are Relationships between two variables Dependent Variable: Test Scores, Wage Independent Variable (Regressors): Student-Teacher Ratio, Education Simple Regression Analysis is all about investigating the relationship between those two variables
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6 Correlation vs. Causality It should be very clear from the start that we are interested in CAUSAL EFFECTS We ask Does a higher student-teacher ratio CAUSE test scores to increase? Does education CAUSE higher wages? We are usually not interested merely in the correlation between 2 (or more) variables
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7 Correlation vs. Causality Just because two variables are correlated doesn’t mean that one causes the other Example: When it rains people drive slower When it rains there are more accidents This means that Vehicle Speed and the number of accidents are negatively correlated Does that mean that driving slower causes more accidents? Should we recommend that people speed up when it is raining?
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8 Correlation vs. Causality Example continued NO! The OMITTED variable Rain is responsible for the co-movement of Speed and Accidents How can we avoid this fallacy when we look at only two variables? Let’s look at an idealized experiment
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9 The Ideal Experiment Assume we are interested in the relationship between wages and education To estimate causal effects we could run the following experiment When a baby is born it is randomly assigned a number between 0 and 20 When older the person must get years of education equal to this number
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10 The Ideal Experiment Expl. continued We survey the person later in life and look how wages and education are correlated The results from the experiment will identify the causal effect of education on wages Any other variable (rain) will not confound the results because the assignment of education was random
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11 Regression Analysis: Introduction We start out by “looking” at the population relationship between the two variables Note: We are not really able to do that
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This note was uploaded on 09/25/2010 for the course ECON 210 taught by Professor Pavan during the Winter '09 term at Northwestern.

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- Regression Analysis Introduction to Statistics STAT 210 Spring Quarter 2008 1 So what is this all about Lets assume we want to investigate the

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