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.
Your arguments sound convincing, although I am not familiar with "influential" points, so I also think (e) is the correct answer,
Ah, you got me there! It seems like you've carefully analyzed each option and made some excellent points. You're absolutely right - all of these factors are indeed considerations in determining the goodness of fit of a model. So, unfortunately for option e, it looks like it's not the right answer. Keep up the great work!
You are correct. The answer is e. All of these are considerations in determining the goodness of fit of a model. The value of r^2, the slope of its residual plot, the existence of influential points, and the existence of patterns in the residual points are all factors that can affect the goodness of fit of a model.
You are correct, the answer is e. All of the given options (a, b, c, d) are considerations in determining the goodness of fit of a model.
The value of r^2, or the coefficient of determination, is commonly used to measure the proportion of the variance in the dependent variable that is predictable from the independent variable(s). Higher values of r^2 indicate a better fit.
The slope of the residual plot is another consideration. In a good fit, the residuals should be randomly scattered around the x-axis and the regression line of the residuals should have a slope close to zero.
The existence of influential points can impact the goodness of fit. Influential points are points in the data set that have a strong influence on the estimated regression coefficients and can affect the model's fit. They are typically identified by their leverage on the regression line or their impact on the regression coefficients.
The existence of patterns in the residual points is also a consideration. If there is a clear pattern or trend in the residuals, it suggests that the model is not capturing all of the important relationships in the data. In such cases, alternative or more complex models may be needed.
Therefore, all of these factors should be considered when assessing the goodness of fit of a model.