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Outlines for today

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Outlines for today Examples of nonlinear relationship Polynomial regression Two statistical concepts in interpretation of nonlinear regressions-- Inflection point – PowerPoint PPT presentation

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Title: Outlines for today


1
Outlines for today
  • Examples of nonlinear relationship
  • Polynomial regression
  • Two statistical concepts in interpretation of
    nonlinear regressions
  • -- Inflection point
  • -- Derivative function for slope
  • Other formats of nonlinear relationships

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Power Transformation
.. Y -gt Y4 Y -gt Y3 Y -gt Y2 Adjust the negative skew
Y -gt Y1
Y -gt Y0.5 Y -gt logY Y -gt -Y-0.5 Y -gt -Y-1 .. Adjust the positive skew
3
Review of Log Transformation
  • logs are exponents logbx y (the log of x to
    the base b is y) means that byx
  • Some examples

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Log Transformation
  • The logarithmic transformation reduces positive
    skewness. Why?
  • Because the logbX function is a function whose
    return value is the power to which b must be
    raised to equal X.
  • For example, log10100 2. Below shows the
    pattern for log base 10

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Examples of nonlinear relationship
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Polynomial Regression
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Quadratic Regression
The best way to interpret the nonlinear
regression results is to plot the relationship.
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?
Y BMI X age
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Inflection Point
  • An inflection point is a point on a curve at
    which the curvature changes sign.

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Find the inflection point
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Calculating the inflection point of a second
order power polynomial
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Slope (using a derivative func.)
  • In a nonlinear regression model, the slope of X
    is not constant but varies with the value of X.
  • A derivative function provides a best
    straight-line approximation to the curve.
  • The slope of X in a nonlinear relationship refers
    to a derivative function of X, which allows to
    vary by X.

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Calculating slope for selected values of X
  • Y .32390 - .00446X .00013 X2
  • where X marital duration in years, and
  • Y of household tasks performed by husband
  • Slope -.00446 2(.00013)X

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Other Nonlinear Models
  • Log-linear
  • Log(Y)b0b1Xe
  • Linear-log
  • Yb0b1log(X) e
  • Log-log
  • Log(Y)b0b1log(X) e
  • Again, the best way to interpret the nonlinear
    regression results is to plot the relationship.

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