LIR 832 - Lecture 5 handout 2

# LIR 832 - Lecture 5 handout 2 - Regression An Introduction...

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1 Regression: An Introduction February 20, 2007 LIR 832 Catching up… ± 1. How to calculate covariances and correlations if you have probability data (grouped data). ± 2. MINITAB: Tables, Covariance, Correlation ± 3. Regression: An introduction

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2 Regression Introduced ± Topics of the day: ± A. What does OLS do? Why use OLS? How does it work? ± B. Residuals: What we don’t know. ± C. Moving to the Multi-variate Model ± D. Quality of Regression Equations: R 2 Regression Example #1 ± Just what is regression and what can it do? ± To address this, consider the study of truck driver turnover in the first lecture…
3 Regression Example #2 ± Suppose that we are interested in understanding the determinants of teacher pay. ± What we have is a data set on average per- pupil expenditures and average teacher pay by state…

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4 Regression Example #2 Descriptive Statistics: pay, expenditures Variable N Mean Median TrMean StDev SE Mean pay 51 24356 23382 23999 4179 585 expendit 51 3697 3554 3596 1055 148 Variable Minimum Maximum Q1 Q3 pay 18095 41480 21419 26610 expendit 2297 8349 2967 4123
5 Regression Example #2 Covariances: pay, expenditures pay expendit pay 17467605 expendit 3679754 1112520 Correlations: pay, expenditures Pearson correlation of pay and expenditures = 0.835 P-Value = 0.000 Regression Example #2 \$0 \$5,000 \$10,000 \$15,000 \$20,000 \$25,000 \$30,000 \$35,000 \$40,000 \$45,000 \$0 \$1,000 \$2,000 \$3,000 \$4,000 \$5,000 \$6,000 \$7,000 \$8,000 \$9,000 Expenditures Avg. Pay

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6 Regression Example #2 The regression equation is pay = 12129 + 3.31 expenditures Predictor Coef SE Coef T P Constant 12129 1197 10.13 0.000 expendit 3.3076 0.3117 10.61 0.000 S = 2325 R-Sq = 69.7% R-Sq(adj) = 69.1% pay = 12129 + 3.31 expenditures is the equation of a line and we can add it to our plot of the data. Regression Example #2 \$0 \$5,000 \$10,000 \$15,000 \$20,000 \$25,000 \$30,000 \$35,000 \$40,000 \$45,000 \$0 \$1,000 \$2,000 \$3,000 \$4,000 \$5,000 \$6,000 \$7,000 \$8,000 \$9,000 Expenditures Avg. Pay Pay = 12129 +3.31*Expenditures
7 Regression: What Can We Learn? ± What can we learn from the regression? ± Q1: What is the relationship between per pupil expenditures and teacher pay? ± A: For every additional dollar of expenditure, pay increases by \$3.31. Regression: What Can We Learn? ± Q2: Given our sample, is it reasonable to suppose that increased teacher expenditures are associated with higher pay? ± H 0 : expenditures make no difference: β 0 ± H A : expenditures increase pay: β >0 ± P( (xbar - μ )/ σ > (3.037 - 0)/.3117) = p( z > 10.61) ± A: Reject our null, reasonable to believe there is a positive relationship.

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8 Regression: What Can We Learn? ± Q3: What proportion of the variance in teacher pay can we explain with our regression line? ± A: R-Sq = 69.7% Regression: What Can We Learn? ± Q4: We can also make predictions from the regression model. What would teacher pay be if we spent \$4,000 per pupil? ± A: pay = 12129 + 3.31 expenditures ± pay = 12129 + 3.31*4000 = \$25,369 ± What if we had per pupil expenditures of \$6400 (Michigan’s amount)? ± Pay = 12129 + 3.31*6400 = \$33,313
9 Regression: What Can We Learn? ± Q5: For the states where we have data, we can also observe the difference between our prediction and the actual amount.

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LIR 832 - Lecture 5 handout 2 - Regression An Introduction...

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