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Unformatted text preview: Econ 139: Introduction to Econometrics Andrew Sweeting 1 Department of Economics Duke University Spring 2011 Econ 139 Handout 6 (Duke) Univariate Regression (2) Spring 2011 1 / 30 A Pharmaceutical Testing Example Let&s look at a real world example. Ritalin has been shown to alleviate symptoms of Attention Decit Hyperactivity Disorder (AD/HD) AD/HD & hyperactivity disorder& Ritalin: CIBAGeigy product; content: methylphenidate Objective is to determine if Ritalin can alleviate symptoms of Central Auditory Processing Disorder (CAPD) Why do we think it might? CAPD has symptoms similar to AD/HD In fact, children often have both (or are misdiagnosed as having one when they actually have the other). 1 1 Further information may be found at http://kidshealth.org/ Econ 139 Handout 6 (Duke) Univariate Regression (2) Spring 2011 2 / 30 Ritalin Example: Experiment So how do we test the e/ectiveness of Ritalin on CAPD? Suppose we do an experiment: 1 Select 64 children who su/er from CAPD 2 Have all children take the same auditory test 3 Give 32 children (treatment group) some dosage of Ritalin 4 Give 32 children (control group) a placebo (i.e. no drug) 5 Have all 64 children retake the auditory test Econ 139 Handout 6 (Duke) Univariate Regression (2) Spring 2011 3 30 Ritalin Example: Data DOSAGE i denotes the dosage of Ritalin received by child i Range = 0 to 0 . 7 mg kg IMPROVE i = (child i &s score on 2 nd test  child i &s score on 1 st test) Range = & 20 to 50 Here are the results displayed in a graph: Econ 139 Handout 6 (Duke) Univariate Regression (2) Spring 2011 4 / 30 Ritalin Example: Regression Results Following our OLS methodology, we assume the average relationship between IMPROVE i and DOSAGE i is linear IMPROVE i = + 1 DOSAGE i + u i Estimating this model using our data, here is what you obtain: or \ IMPROVE = . 23 + 12 . 18 & DOSAGE Econ 139 Handout 6 (Duke) Univariate Regression (2) Spring 2011 5 / 30 Ritalin Example: Interpretation So how do we interpret 1 ? For an additional 1 unit & mg kg increase in Dosage, Improve increases by 12.18. More appropriately: for an additional 0.1 mg kg increase in Dosage, we expect Improve to increase by 1.218. But does this tell us that Ritalin has a signi&cant impact on CAPD? What does signi&cant mean? We need to perform a hypothesis test, and to do this, we need to know SE ( b 1 ) (then it will be easy). So we need to derive the distribution of the b &s. But rst, are the b &s unbiased? Let&s prove that they are. Econ 139 Handout 6 (Duke) Univariate Regression (2) Spring 2011 6 / 30 Sampling Distribution of the OLS Estimators OLS is unbiased Now it&s time to do some signicant algebra: we& ll take it slowly!...
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This note was uploaded on 08/02/2011 for the course ECON 139 taught by Professor Alessandrotarozzi during the Spring '08 term at Duke.
 Spring '08
 ALESSANDROTAROZZI
 Econometrics

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