It depends on the purpose of the model, if you need a "prediction tool" or if you want a model representing your knowledge about functional relationships between different factors (which can be used for prediction, too, but can also help improving our theoretical understanding of the underlying processes as well as help in inductive reasoning).

Yes, stepwise selection procedures are dangerous. Any procedure that tries to rate the quality of a model only with data that was used to build and fit the model are dagerous, because they are bound to the observed data and therfore tend to overrate specific ("random") patterns in the observed data that usually won't generalize well. They also usually start on a very restricted set of possible models, neccesarily accounting only for the variables you have actually observed (missing variable bias) and often accounting only for linear relationships (failing to include the appropriate class of models), no or only lower-order interactions (kind of missing variable bias) and so on.

If it comes to prediction, you can only judge the performance of a model based on independent data. Using the result of this to modify or further select a model destroys this independence. This also applies to the cross-validation techniques. Having an independent set of data (aka test-set), it actually does not matter how you came up with your model (using a traing-set, pure intuition, or some theory). You show how well it works in the test-set, and this is it. This independence is difficult to achieve. If you have one large set of data, gerenerated under kind of homogeneous conditions, this set may contain specific, irrelevant "random" patterns that your model-builing process will try to capture. Dividing this data into a training-set and a test-set (afasik this is pretty much the standard today) just generates a test-set with the very same random patterns and you will overestimate the performance of your model.

My purpose with the dataset is more to the second one you have mentioned - to understand the underlying processes among the variables. Thank you very much for your comment, this will help me to explore more.

a good regression model fulfills all the assumptions of the regression assumption. The alignment of the regression model can be explained by using the larger r2 value, the better the model. If the value is close to 1 then the regression model is good. The value of r2 has characteristics including: 1) is always positive, 2) the maximum r2 value is 1. If the r2 value is 1, it will have a perfect balance.

Two (o more) different sets of variables can explain the same R2 value. And it’s possible that other regression models (even nonlinear, as polynomial one) cause a similar effect. Therefore, you can test several models to explain the causal relationship between variables, but you must also have a good theoretical model: perhaps it’s the most important base to built an adequate statistical model.

Let's start at the beginning. First, explore your data. Look at the distributions of each variable and check for errors and outliers. You didn't say whether you had identified the dependent (y) variable you hope to model. You need to do that based on your understanding of the data and what you want to accomplish. (See Jochen's comment).

Then make scatterplots of that dependent variable against each of the proposed predictors. Now, if the distribution of y is skewed and/or if the shape of plots of y against the x's are not straight, consider re-expressions. Start by re-expressing y. Chances are the same re-expression will both improve its distribution and make plots against the x's more nearly straight. You can't fit a (linear) regression to curved data.

If there are outliers in the scatterplots (after re-expressing) then you'll need to deal with them (either by correcting them or setting them aside). After you've done all these things, you may already have a better understanding of your data. Select one or more predictors and compute the regression. I agree that stepwise methods should be avoided. Once you fit a regression model, examine the residuals. Your goal should be a clean model that makes sense not just a high R2.

Finally, if you are particularly interested in one or two coefficients in your model, make partial regression plots for those to understand how they affect your model.

First step in solving this... the nitty-gritty about Regression Analysis is required here!

I think you may need this👇

https://online.stat.psu.edu/stat501/

Elisha J Inyang Thank you very much for sharing with me.

Very late to the party but for predictions I like the attached method the most. Best wishes David Booth

Oliur Rahman Tarek -

Besides David's recommendation, I suggest that you not ignore your subject matter expertise.

The sample you select may be problematic, so that a "graphical residual analysis" may show a tight fit, but you can actually overfit to that sample, so a "cross-validation" may be helpful. If you have enough data (hopefully from various parts of the population), you could just do a graphical residual analysis for each of several samples, one sample per scatterplot, every alternative model used for each scatterplot.

I caution against the use of transformations. They can make interpretation less clear.

If you have outliers, you should try to identify them, but not be quick to throw out something because it is inconvenient. However, if you have enough questionable data, which cannot be identified from your data collection as definitely outliers, you might use robust regression, though I'd think that would be a last resort.

You may notice heteroscedasticity in your graphical residual analyses. Sometimes you have the same range in the y-direction, but if the density in the same range is less, that is increased variance, nevertheless. Heteroscedasticity is a feature to be expected, not a bug. See https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression, and the various updates and references there, including updates about not using transformations or hypothesis tests.

Best wishes - Jim

Thank you David Eugene Booth and James R Knaub for sharing your knowledge with us.