Stepwise Regression

Stepwise regression is a step-by-step process of constructing a model by introducing or eliminating predictor variables. First, the variables undergo T-tests and F-tests. Then, predictor variables are individually tested to fit a linear regression model.

The stepwise selection procedure employs software packages specifically designed to test models. Some of these models comprise hundreds of variables. However, there are certain limitations—errors and inconsistencies are witnessed in the statistical significance stage. Stepwise regression, python, and other programming languages are closely interlinked.

• The Stepwise regression model is constructed bit by bit—by adding or removing predictor variables. There are primarily three types of stepwise regression, forward, backward and multiple.
• Usually, the stepwise selection is used to handle statistical data handling. Stepwise selection simplifies complicated calculation models by feeding only the right variables (relevant to the desired outcome). Other variables are discarded.
• “Stepwise regression in r" signifies the model for different subsets of data. In SPSS, stepwise regression is used to perform residual analysis; the model's accuracy is checked.

Stepwise regression is used to design a regression model to introduce only relevant and statistically significant variables. Other variables are discarded. However, every regression calculation contains unwanted variables. These variables are predictive and complicate the process unnecessarily.

Therefore, a stepwise selection analysis eliminates variables irrelevant to the model. To separate variables, F-tests and T-tests are conducted. In addition, other tests that offer optimal usage can also be selected for the model.

A regression model describes the relationship between variables. The given variable could be an independent, dependent, response, or target variable. For example, if a relationship between height and weight is studied, it is referred to as a linear regression model.

Logistic stepwise regression depends on the nature and size of variables. These variables undergo testing—whether they are relevant to the given model. It can be a time-consuming process; each individual is tested independently. Therefore analysts use software packages (defined to test variables automatically) to save time.

The whole process is done bit by bit—the variables are reported only when they are by the set parameters. The process can be employed in any linear or logistic stepwise regression model.

As expected, there is certain criticism against this method. For example, some statisticians find stepwise selection biased; it focuses excessively on one model.

The method is further divided into the following subtypes.

#1 - Forward Stepwise Regression

The forward model is empty with no variable. Instead, each predictor variable is first tested and then introduced into the model. Only the ones that meet statistical significance criteria are kept.

This process is repeated till the desired result is acquired. It is called forward regression because the process moves in the forward direction—testing occurs toward constructing an optimal model.

#2 - Backward Stepwise Regression

It is the opposite of 'forward regression.' When the backward approach is employed, the model already contains many variables. Each variable then undergoes testing—variables that fail to meet statistical significance standards are discarded. This process is repeated for all the variables till the desired result is obtained.

#3 - Bidirectional Stepwise Regression

The bi-directional approach is simply a combination of forward and backward regression. It is naturally a tad bit complicated. Nevertheless, analysts use this challenging subtype to save time when too many variables are present.

Let us look at some examples to understand regression better.

Example #1

Joel is traveling with a single bag—he can only carry a specific amount of weight—thirty kilograms. Currently, Joel's luggage weighs thirty-nine kilograms. Therefore, he is asked to reduce the extra weight by removing some items.

Joel opens his bag and is now confused; he is not sure which item should be dropped and which ones should be taken. More importantly, the volume of each item is obvious, but he is not entirely sure which object weighs more and which ones less.

Joel attempts a trial-and-error approach. He first attempts to remove some items and weighs the bag. With multiple trials, he comes close to the allowed thirty-kilogram limit. The removed articles included—mini gadgets, a pair of shoes, his leather jacket, and some books.

In a way, Joel remodeled his bag for the desired weight. This was a simplified example of stepwise selection. Here, Joel was the analyst, the shoes, books, and gadgets were variables, the bag was the model, and the required result was thirty kilograms. To be precise, Joel used the backward elimination method to ensure that the right variables fit the model.

Alternatively, Joel could have attempted a forward regression approach. In that case, he would start with the required outcome—thirty kilograms of weight. He would then move forward to construct a model (fill the bag with items). Joel can achieve this by weighing each item individually and then deciding which ones to drop and which to include.

Example #2

The approximation of a two-variable function is another example of stepwise selection. The forward selection approach is commonly used when the model's coefficients are set to zero. Next, variables are introduced into the model, one by one. At first, the coefficients are zero; later, a specific variable is chosen to fit the model perfectly.

In contrast, the other variables can opt for different factors, say, the highest correlation. Some less common regression subtypes are metaheuristic optimization and Takagi-Sugeno Fuzzy systems.

Stepwise selection is used for the following purposes.

• Construct a model containing only related variables (with required statistical significance).
• “Stepwise regression in r" signifies the model for different subsets of data.
• The method eliminates unnecessary variables from the model—to make it a perfect set.
• In SPSS, stepwise regressions are used to perform residual analysis; the model's accuracy is checked. SPPS is a software suite used in the study of social sciences.
• In some cases, the stepwise selection is repeated to ensure the model's accuracy (when dealing with a critical subject).

This article has been a guide to What is Stepwise Regression. We explain its types, examples, and uses in Python and SPSS. You can learn more about it from the following articles -

• Multiple Linear Regression
• Logistic Regression vs. Linear Regression
• Regression to the Mean