Class 7. Categorical variables: more than two groups.

What you need to have learnt from Class 6.

Two types of model.

Parallel lines model: different intercepts - same slopes.

Non-parallel lines: different intercepts and different slopes.

Two key facts in understanding the JMP output.

JMP always makes comparisons to the ``average'' of the groups.

JMP always leaves one group out - you figure out the missing difference (easy).

Non-parallel slopes, an interaction model.

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 a variable with three groups (G1,G2,G3).

Parallel lines regression - Three of them, one for each group.

Key fact: 3 groups, JMP gives 2 comparisons.

G1 to average.

G2 to average.

You work out G3: if G1 is 4 above average and G2 is 3 above average then G3 must be 7 below average.

Rule: what number added to the others makes them all sum to zero?

A negative on a categorical variable coefficient -- BELOW par.

A positive on a categorical variable coefficient -- ABOVE par.

Non-parallel lines - 3 different intercepts and three different slopes.

Presenting categorical variable regression, an equation for each group. Follows p.218 in the bulk pack.

Baseline: RunTime =  179.59            +  0.23 RunSize
G1      : RunTime = (179.59 +  22.94)  + (0.23 + 0.07) Runsize
G2      : RunTime = (179.59 +   6.90)  + (0.23 + -.10) Runsize
G3      : RunTime = (179.59 + -29.84)  + (0.23 +  .03) Runsize

Is a difference significant? Look at the t-stat.

Are the differences significant? Look at a partial-F (``effect test'' in JMP).

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).

Strategy for when some groups are significantly different and others are not: collapse the non-significant groups together.

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.

Interaction with more than one variable - fine (see p. 209).