Nonlinear Regression Functions

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Chapter 8

• Nonlinear Regression Functions

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Nonlinear Regression Functions(SW Chapter 8)
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The TestScore STR relation looks linear (maybe)
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But the TestScore Income relation looks
nonlinear...
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Nonlinear Regression Population Regression
Functions General Ideas (SW Section 8.1)
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The general nonlinear population regression
function
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Nonlinear Functions of a Single Independent
Variable (SW Section 8.2)
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1. Polynomials in X
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Example the TestScore Income relation
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Estimation of the quadratic specification in
STATA
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Interpreting the estimated regression function
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Interpreting the estimated regression function,
ctd
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Estimation of a cubic specification in STATA
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Summary polynomial regression functions
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2. Logarithmic functions of Y and/or X
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The three log regression specifications
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I. Linear-log population regression function
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Linear-log case, continued
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Example TestScore vs. ln(Income)
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The linear-log and cubic regression functions
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II. Log-linear population regression function
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Log-linear case, continued
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III. Log-log population regression function
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Log-log case, continued
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Example ln( TestScore) vs. ln( Income)
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Example ln( TestScore) vs. ln( Income), ctd.
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The log-linear and log-log specifications
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Summary Logarithmic transformations
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Other nonlinear functions (and nonlinear least
squares) (SW App. 8.1)
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Negative exponential growth
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Nonlinear Least Squares
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Interactions Between Independent Variables (SW
Section 8.3)
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(a) Interactions between two binary variables
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Interpreting the coefficients
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Example TestScore, STR, English learners
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(b) Interactions between continuous and binary
variables
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Binary-continuous interactions the two
regression lines
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Binary-continuous interactions, ctd.
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Interpreting the coefficients
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Example TestScore, STR, HiEL (1 if PctEL ? 10)
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Example, ctd Testing hypotheses
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(c) Interactions between two continuous variables
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Interpreting the coefficients
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Example TestScore, STR, PctEL
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Example, ctd hypothesis tests
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Application Nonlinear Effects on Test Scores of
the Student-Teacher Ratio (SW Section 8.4)
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Strategy for Question 1 (different effects for
different STR?)
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Strategy for Question 2 (interactions between
PctEL and STR?)
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What is a good base specification?
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Tests of joint hypotheses
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Interpreting the regression functions via plots
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Next, compare the regressions with interactions
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Summary Nonlinear Regression Functions