Question

Which of the following is not a consideration in determining the goodness of fit of a model?

a. the value of r^2
b. the slope of its residual plot
c. the existence of influential points
d. the existence of pattern in the residual points
e. all of these are considerations

I think the answer is e.

a. Since r^2 is a common method of 'measuring' the goodness of fit,
obviously this cannot be a correct answer option.

b. If the regression is 'good', then the residuals will cluster about the
x-axis, or at least average the x-axis. A regression line for the
residuals, then, should have a slope of or about m = 0. So this IS a
consideration.

c. Influential points are not outliers; they cannot safely be discarded. They tend, by their nature, to reduce the ability of the modelling method to produce a good fit, but only in comparison to the data set without that point.

d. If there is a pattern, then probably some other sort of regression would be a better fit. So looking for a pattern IS a consideration, and this
cannot be a correct option.

Answer 1

Your arguments sound convincing, although I am not familiar with "influential" points, so I also think (e) is the correct answer,