Stat 601, Fall 2000, Class 9




What you need to have learnt from Class 8

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Two types of model.
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Parallel lines model: different intercepts - same slopes.
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Non-parallel lines: different intercepts and different slopes.
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Two key facts in understanding the JMP output.
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JMP always makes comparisons to the ``average'' of the groups.
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JMP always leaves one group out - you figure out the missing difference (easy).
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Non-parallel slopes, an interaction model.
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Interaction. A three variable concept (Y,X1,X2). Generic description: the impact of X1 on Y depends on the value of X2.

New material for today: more than two groups.

Example consider three groups (G1,G2,G3).

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Parallel lines regression - Three of them, one for each group.
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Key fact: 3 groups, JMP gives 2 comparisons.
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G1 to average.
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G2 to average.
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You work out G3: if G1 is 4 above average and G2 is 3 above average then G3 must be 7 below average.
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Rule: what number added to the others make them all sum to zero?
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A negative on a categorical variable coefficient say BELOW par.
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A positive on a categorical variable coefficient say ABOVE par.
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Non-parallel lines - 3 different intercepts and three different slopes.
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Presenting categorical variable regression, an equation for each group. Follows p.194 in the bulk pack.
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         Baseline: RunTime =  179.59           +  0.23 RunSize
         G1      : RunTime = (179.5 +  22.94)  + (0.23 + 0.07) Runsize
         G2      : RunTime = (179.5 +   6.90)  + (0.23 + -.10) Runsize
         G3      : RunTime = (179.5 + -29.84)  + (0.23 + -.03) Runsize
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Is a difference significant? Look at the t-stat.
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Are the differences significant? Look at a partial-F (``effect test'' in JMP).
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The partial-F 
        /    2                 2     \     /Number of 
       |    R        -        R      |    / variables
        \    BIG               SMALL /   / in the subset.
        __________________________________________________________________

         /                      2     \     / Number of observations
        |    1        -        R      |    / minus number of parameters
         \                      BIG   /   / in Big model. (inc. intercept).
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Strategy for when some groups are significantly different and others are not: collapse the non-significant groups together.
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More than one categorical variable - fine. (e.g. gender and race). What does a parallel lines regression mean here? Take Y as income and explain it in English.
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Interaction with more than one variable - fine (see p. 186).

Project discussion

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What the report should look like?
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Model building strategies
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Start with marginal analyses
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Start small, build up
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Start large, cut away
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Force in terms you want to talk about
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Start with a ``map'' - interesting questions
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What makes a good model?
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Do you have a good model?
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Prediction vs. interpretation
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Interpreting the regression coefficients
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The 1/units term
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Economic considerations - labor, capital and materials
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Answer questions and provide insight
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How is the New Plant doing?
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Who do we learn from for best practices?
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Is this a labor intensive process?
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Where are the opportunities to control costs
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Should this model even be used for giving quotes?
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Are there key pieces of information missing?
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Plant or managers?



2000-12-02