Yes, if you define percisely what you mean with "goodness of fit". If you define "goodness of fit" as something measured by AIC (or R², or, RMSE, or whatever), then AIC (or R², or, RMSE, or whatever) is a measure of this goodness of fit. That's trivial and not really helpful.

Same if you talk about "model performance". How do do define it, precisely?

Usually, these terms relate to complex properties that -as the word "complex" indicates- cannot be summarized in a single numerical measure. It's like describing a car, or a house, or a city, or a person, etc. with just a single numerical measure. This may surely provide a piece of information on one aspect, possibly even some important aspect, but it is never sufficient to get a useful description of the car, the house, the city, the person, etc.

And one should also keep in mind that models can have different purposes, and relevant aspects of the "model performance" are related to these purposes. So even some set of measures cannot be a general solution, as it all depends on the purpose of the model and the scientific context it is embedded in. Talking about model performance disregarding that context is like talking about positions or velocities of objects in empty space with no reference: it's rather meaningless.

In addition to Prof Wilhelm reply see the attached screenshot for details . Available in the z-library. best wishes David Booth

The goodness of fit of a statistical model describes how well it fits a set of observations. Measures the realtionship between observed values and the values expected that measures can be used in statistical hypothesis testing such as test for normality of residuals, to test whether two samples are drawn from identical distributions such as Kolmogorov–Smirnov test or whether outcome frequencies follow a specified distribution like Pearson's chi-square test.

Manojit -

First, I'd like to point out that R-squared, though popular, can be very misleading. For one thing, in https://data.library.virginia.edu/is-r-squared-useless/, they note that it is not a measure of fit. I suppose that one way to look at it is that the sigma (which generally should become larger with larger associated predicted-y) for epsilon is the "irreducible" error, and one can have a model which does "fit" the behavior of the data well, except for a large sigma for the estimated residuals which makes R-squared small.

But yes there are many measures, but if you want to understand more about how your model fits your data, you need graphics. A "graphical residual analysis" (you can research this term) will show you where and how your model fits, for your specific sample. Further, you may need to check this for other samples, or do some other kind of "cross-validation," because, please note ...

...any measure of fit, or even a graphic giving a better overall 'picture,' is only with regard to the sample drawn.

Having a better 'fit' for your model to that sample is not necessarily good! If you fit too closely to a sample, your model may fit less well for the remainder of the population or subpopulation you are trying to model.

Multiple regression is tricky. If, for the population or subpopulation you wish to model, you leave out an important variable, you may have substantial omitted variable bias. If you include variables you don't need you may substantially increase variance. Obtaining exactly the right predictor variables, no more, no less, and just the right ones, is important. Because of collinearity and other issues, one may not obtain 'ideal' predicted-y values, but using principal components means giving up on explaining much about the helpfulness of the predictors, and their subject matter importance. Graphics can be used, to an extent, to show each predictor's usefulness, but in multiple regression when they work together, they impact one another. Further, they can be used in various functions. So even if you know the individual impact of each predictor on a response variable, the combined impact in a multiple regression may be surprising. (One predictor or function of some predictors may be graphed against another predictor or function of some predictors to check for collinearity.) "Nonessential heteroscedasticity," perhaps from an omitted variable or stratification issue, may occur, but if you obtain close to ideal predicted-y, and model for appropriate population divisions, with good quality data, there should be "essential heteroscedasticity" where residual sigma increases with increasing associated predicted-y values. This should be modeled with regression weights impacting regression coefficients, and will generally show in the graphical residual analyses.

Summary: When investigating fit, graphical residual analyses are important for an overall view. Consider your subject matter knowledge when constructing alternative models. Also, avoid overfitting to your sample; consider cross-validation.

Cheers - Jim

PS - When I said that "...one can have a model which does 'fit' the behavior of the data well, except for a large sigma for the estimated residuals which makes R-squared small," perhaps I can explain that better as the difference between the confidence intervals for means, versus the prediction intervals for other members of the population or subpopulation being modeled. Such confidence intervals do not include a term for sigma for the estimated residuals as a separate and additional term the way that the prediction intervals do. Please see the following:

https://online.stat.psu.edu/stat501/lesson/3/3.2

https://online.stat.psu.edu/stat501/lesson/3/3.3

Thus, one may model the mean values well, but have a small R-squared.

There is the model part of a regression, and the estimated residual part. R-squared does not tell you about the fit of the model part.