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).
Quadratic Residual Model. To further analyze the fiteffect, we performed a quadratic residual regressionmodel. Studying squared residuals is an alternative tothe absolute residuals model. However, a quadraticmodel is more useful because it allows estimating of first- and second-order effects simultaneously; itincludes squared residuals, but at the same time itallows for more specific testing of the optimality conditionsof the fit model. The quadratic residual model is asfollows:Performance = b0 + b1e + b2e2,where Performance refers to either strategic or financialperformance; e refers to the residuals from the fit model;and b0, b1, and b2 are the regression coefficients of thequadratic model. This is a parabolic function, and weobtain the maximum value of performance at e =–b1/(2b2), if b2 < 0 (required for the parabola to opendownward so that the function is convex with onemaximum). Therefore, if b1 = 0, we obtain the maximumat e = 0. Thus, the advantage of the quadraticmodel is that we can test statistically (1) whether fitmatters generally (significant model fit), (2) whether abetter fit implies better performance (b2), and (3)whether firms in general over- or understandardize marketingstrategies (or use too much or too little breadthfor product offering) with respect to performance (b1).
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