The common form is the presentation of regression equation, with the coefficients of determination and p value included in the brackets. But we know that the beta coefficients and sum of squares and others are also important. So how to present the complete results of stepwise regression?
For any regression (doesn't really matter if it's stepwise or not) there are many ways you could present information about it. You could have a table (or series of tables) presenting key information; you could describe the statistics in prose; you could share the dataset and reproducible code (in something like an RMarkdown notebook); you could make a graph of the coefficients as in this paper (see Figure 3, attached here). It depends on what information you want to highlight, and how.
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Also note that just showing results related to coefficients is not the "complete" results of a regression. There are many other results that may also be relevant to the description of a regression model (such as goodness-of-fit measures). Also, some different pieces of information are representing the same thing or are even straightforward transformations of other ones (for example, unstandardized coefficient, standardized coefficient, standard error, t-statistic, and p-value might all be shown in a table of regression results, but many of those are dependent on each other, so if you show all of them you are essentially duplicating information); likewise, there are many different goodness-of-fit measures (like AIC, BIC, -2LL, etc.) and some are just direct transformations of each other (e.g., some software may output both "deviance" and "-2LL", which are not really different things; if you know one, you know the other). Thus, if "the complete results" means every possible number and statistic about this regression one could extract, then no one would ever want to present "the complete results", as it would take up a huge amount of space and include a lot of redundant information.
In multiple regression problems, one often has available a large number of candidate explanatory variables. For example, in predicting the sales price of a house, there are generally a multitude of housing (and location) attributes that could potentially influence this price. While it is in principle possible to run all possible regressions, and compare their prediction ability in terms of adjusted R-square, this is practically impossible in most cases (for example 10 explanatory variables yield 10 2 1024 = possible regression models).1 One practical procedure for “searching” the space of possible models is stepwise regression. (Is continued: https://www.seas.upenn.edu/~ese302/extra_mtls/STEPWISE_REGRESSION.pdf)
@Vitalina. It was practical it just didn't work. Please read my paper. David Booth
@ Stephen. According to your answer, various forms can be used, and it is not possible to present the "complete" results. Thanks for your response.
@ David Eugene Booth and Vitalina Babenko. Thank you very much for the reply. The paper is very helpful for me.
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