AS 737 Categorical Data Analysis

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AS 737 Categorical Data Analysis

• Week 5

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Multiple Logistic Regression
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Multiple Logistic Regression
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Multiple Logistic Regression
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The Logistic Regression Model

• The "logit" model solves these problemsln?
  /(1- ?) ?? ?X e
• ? is the probability that the event Y occurs,
  p(Y1)
• ? /(1- ?) is the "odds ratio"
• ln? /(1- ?) is the log odds ratio, or "logit"
• The logistic distribution constrains the
  estimated probabilities to lie between 0 and 1.
• The estimated probability is ? 1/1
  exp(-? - ? X)
• if you let ? ? X 0, then ? .50
• as ? ? X gets really big, ? approaches 1
• as ? ? X gets really small, ? approaches 0

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• Interpretation of the parameters
• If p is the probability of an event and O is the
  odds for that event then
• the link function in logistic regression gives
  the log-odds

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Newton - Raphson
Newton and Raphson used ideas of the Calculus to
create a method to find the zeros of an arbitrary
equation
Let r be a root (also called a "zero") of f(x),
that is f(r) 0. Assume that            
Let x1 be a number close to r (which may be
obtained by looking at the graph of f(x)). The
tangent line to the graph of f(x) at (x1,f(x1))
has x2 as its x-intercept.
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Newton - Raphson
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Newton - Raphson
From the previous picture, we see that x2 is
getting closer to r. Calculations give
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Using Newton-Raphson Solve
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The Answer for f(x)0
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Find the maximum or minimum for the following
function
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The Answer for the maximum or minimum
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Newton Raphson for Maximization
Taylor Series Expansion
Take the derivative to maximize the function
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Find the square root of 5. Using Newton Raphson
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The Square root of 5 is