Quadratic Residual Model. To further analyze the fit
effect, we performed a quadratic residual regression
model. Studying squared residuals is an alternative to
the absolute residuals model. However, a quadratic
model is more useful because it allows estimating of first- and second-order effects simultaneously; it
includes squared residuals, but at the same time it
allows for more specific testing of the optimality conditions
of the fit model. The quadratic residual model is as
follows:
Performance = b0 + b1e + b2e2,where Performance refers to either strategic or financial
performance; e refers to the residuals from the fit model;
and b0, b1, and b2 are the regression coefficients of the
quadratic model. This is a parabolic function, and we
obtain the maximum value of performance at e =
–b1/(2b2), if b2 < 0 (required for the parabola to open
downward so that the function is convex with one
maximum). Therefore, if b1 = 0, we obtain the maximum
at e = 0. Thus, the advantage of the quadratic
model is that we can test statistically (1) whether fit
matters generally (significant model fit), (2) whether a
better fit implies better performance (b2), and (3)
whether firms in general over- or understandardize marketing
strategies (or use too much or too little breadth
for product offering) with respect to performance (b1).