LIR 832 Lecture 7 notes 3 slides

LIR 832 Lecture 7 notes 3 slides - Regression Continued LIR...

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1 Regression Continued… LIR 832 March 20, 2007 Review: What Do These Regression Terms Mean? Regression Analysis: weekearn versus Education, age, female, hours The regression equation is weekearn = - 1053 + 65.1 Education + 7.07 age - 230 female + 18.3 hours 44839 cases used 10319 cases contain missing values Predictor Coef SE Coef T P Constant -1053.01 19.43 -54.20 0.000 Educatio 65.089 1.029 63.27 0.000 age 7.0741 0.1929 36.68 0.000 female -229.786 4.489 -51.19 0.000 hours 18.3369 0.2180 84.11 0.000 S = 459.0 R-Sq = 31.9% R-Sq(adj) = 31.9% Topics of the Day… ± 1. Populations and samples in the context of regression. ± 2. The distribution of the error term in a regression model. ± 3. Hypothesis testing. ² One-tailed. ² Two-tailed. ± 4. Tests of group variables.
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2 Review: Populations and Samples ± In earlier lectures, we learned that there is a true parameter in a population ( µ ) that we try to estimate by a sample (x- bar). In regression, there are similarities. ± In other words, there is a “true” relationship between the variables in the population that we are trying to estimate: y i = β 0 + β 1 *X 1i + ε i . ± Since we often cannot see the entire population, we estimate this relationship through finding the equation within a sample: or yX e ii i =+ + $$ ββ 01 1 ybb X e i + 1 Review: Populations and Samples ± As with all sample results, there are lots of different samples which might be drawn from a population. ± These samples will typically provide somewhat different estimates of the coefficients. ± This is, once more, a byproduct of sampling variation. Review: Populations and Samples ± Estimate a simple regression model of weekly earnings for all of the data on managers and professionals (what we’ll consider as the “population”), then take random 10% sub-samples of the data and compare the estimates. ² Weekly Earnings = β 0 + β 1 * education + ε ± Upon generating five random sub-samples of the data, we find the following:
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3 Review: Populations and Samples Estimate β 0 (Intercept) β 1 (Coefficient on Education) POPULATION -484.57 87.49 Sample 1 -333.24 79.21 Sample 2 -488.51 88.16 Sample 3 -460.15 85.93 Sample 4 -502.18 88.44 Sample 5 -485.19 87.88 Populations and Samples ± Important point: ² Sampling variability is responsible for the fact that the sample regression coefficients do not exactly reproduce the population regression coefficients, which is what we are after. ± Q: Why does this happen? ² A: We pull samples out of populations. We typically take a single sample. But, in fact, there are many many samples we could pull from a given population. Populations and Samples: Example ± Q: How many unique samples (no two samples have the exact same individuals) in a population of 15 with sample size 5? ± A: 15 5 15 51 0 ! 3003 C == ! !* ,
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4 Populations and Samples: Example #2 ± Q: Now suppose we are taking samples of 5,000 from our 50,000-person data set on managers and professionals. How many unique samples can we draw? ± A: ± As a result, we have many possible samples upon which to estimate a regression model. This will produce many different sample regression coefficients (b)… which may be different than the population coefficients ( β ).
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LIR 832 Lecture 7 notes 3 slides - Regression Continued LIR...

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