0

I have performed a regression analysis and on top of computing the coefficients, confidence intervals, and significance, I have the standard errors.

I have been asked to provide a numerical estimate of the goodness of fit for the models to the data. WIll these standard errors suffice?

I'm not sure how to interpret them though.

EDIT:

In light of my understanding of the distinction between the SE of coefficients and the SE of the regression, is there any way of calculating the SE of the regression given the SE of the coefficients?

EDIT:

Regarding the difference between standard error of the regression and standard error of the coefficients, this excerpt from link explains it quite well:

In general, the standard error of the coefficient for variable X is equal to the standard error of the regression times a factor that depends only on the values of X and the other independent variables (not on Y), and which is roughly inversely proportional to the standard deviation of X. Now, the standard error of the regression may be considered to measure the overall amount of "noise" in the data, whereas the standard deviation of X measures the strength of the "signal" in X. Hence, you can think of the standard error of the estimated coefficient of X as the reciprocal of the signal-to-noise ratio for observing the effect of X on Y. The larger the standard error of the coefficient estimate, the worse the signal-to-noise ratio--i.e., the less precise the measurement of the coefficient.

Brad
  • 41
  • 1
  • 6
  • See: http://stats.stackexchange.com/questions/131267/weka-result-interpretation/131273#131273 for learning about measures related to SE. – Tim Apr 27 '15 at 12:55
  • Thanks, just read it. So if I wanted to calculate RMSE (SE of the regression) from the SE of the coefficients what do I do? Also, how do I establish if the model fits well from an RMSE value. Don't I need a comparator or some significance test? – Brad Apr 27 '15 at 13:31
  • All the error-based measures are relative - so they could help if you have two models estimated on the same dataset and want to compare them. There is no "cutoff" value for "good" or "bad" model in here. – Tim Apr 27 '15 at 13:34
  • OK understood. Any way though of calculating the regression SE from coefficient SEs? – Brad Apr 27 '15 at 13:38
  • No, those are different things - check the link I provided for definition of residuals (model errors). – Tim Apr 27 '15 at 13:42
  • Ok I understand that they are different but in the absence of the raw data but only the SE of coefficients, is it possible to calcualte the model error from the coefficient errors? – Brad Apr 27 '15 at 14:07
  • Let us [continue this discussion in chat](http://chat.stackexchange.com/rooms/23231/discussion-between-tim-and-brad). – Tim Apr 27 '15 at 16:15

1 Answers1

1

"Goodness of fit" is a general term that basically tries to summarize the predictive strength of the model as a whole. Depending on the type of regression, typical measures are the

  • R-squared,
  • the AIC,
  • the standard deviation of the residuals,
  • mean squared prediction errors,
  • mean absolute prediction errors,
  • the global F-statistics etc.

These figures you do not find in the effects table (with coefficients, standard errors of the coefficients, t-values etc.). All statistical packages provide this kind of information in some way though.

Michael M
  • 10,553
  • 5
  • 27
  • 43
  • So the standard errors of the coefficients do not are a completely different type of information that in no way relate to model fitting? – Brad Apr 27 '15 at 12:33
  • It is probably not what they expect. Although the standard errors of the coefficients tend to be (comparatively) small if the goodness of fit measures are "good". – Michael M Apr 27 '15 at 12:35
  • Ok thanks. I read here at the bottom [link](http://uk.mathworks.com/help/curvefit/evaluating-goodness-of-fit.html) that the RMSE is also called standard error of the regression. Is that different from standard error of the coefficient? – Brad Apr 27 '15 at 12:37
  • I'm now wondering if I can calculate the SE of the regression from the SE of the coefficient? – Brad Apr 27 '15 at 12:52