# THREECV1 Regression Analysis

[From Rick Marken (950118.1430)]

Me:

Why not use the multiple regression capabilities of Minitab to find the
relative contribution of each of these variables to the variance in H?

Bruce Abbott (950117.0930 EST) --

Why, do you think it will tell us something about how subjects control? (;->

I think that such an analysis (such as the one shown below) will tell us
nothing about control and that what it does tell us will be completely

Bruce Abbott (950117.1145 EST) --

Just to make Rick Marken happy, here is a Minitab multiple regression
analysis of the THREECV1 data.

Thank you:-)

Here are the results:

The regression equation is
H = - 150 + 0.426 C1 + 0.501 C2 - 0.456 C3

Predictor Coef Stdev t-ratio p
Constant -150.13 74.42 -2.02 0.044
C1 0.42566 0.01829 23.27 0.000
C2 0.50106 0.01919 26.12 0.000
C3 -0.4558 0.2334 -1.95 0.051

s = 33.13 R-sq = 69.9% R-sq(adj) = 69.7%

The B weights in the regression equation don't tell us much, though it is
interesting that the regression analysis did pick up the fact that the
relationship between the controlled cursor, C3, and the handle, H, is
negative (note that the raw correlation between C3 and H is positive - -
.013). Note also that the only predictor of H that would be REJECTED by a
conventional statistical test as not significant (p<.05) is C3 -- the
controlled cursor. Only C1 and C2 (and the regression constant) would be seen
as significant (non-chance) contributors to the variance in H; in fact, C2
and C3 had nothing at all to do with the variations in H made by the subject.

The most telling analysis would be to look at the the proportion of variance
in H that is accounted for by each predictor variable. It would be nice if
you could report this data, Bruce (using stepwise regression, perhaps). I bet
that about 34% of the variance in H is accounted for by C1, another 34% by C2
and less than 1% by C3 -- the only variable that is ACTUALLY contributing to
the variance in H.

Why not show the results of this analysis to some psychologists and ask
them which of the three independent variables, C1, C2 or C3, made the
greatest contribution to the subject's behavior, H. How many psychologists
would conclude that C3 made the greatest contribution? If any do pick C3,
would you say that they are qualified to teach behavioral data analysis