How do you handle multivariate regression?

The first step is to rule out collinearity between the response variables and the main variable. This can be done in R or Phyton - High R2 but none of the predictors is significant, there is collinearity. Second is the determination of the predictors with their determined weight (WoE and Information value), which will tell us what weight each variable will have according to its predictive capacity and those that are duplicated are discarded.

Selecting the right multivariate regression model hinges on our dependent variable: Use a Linear Model for continuous outcomes. Opt for a Logistic Model for binary outcomes. Choose a Multinomial Model for outcomes with multiple categories. Be mindful of the number of independent variables to avoid overfitting or underfitting. Consider adding interaction or polynomial terms for complex or nonlinear relationships. This step sets the stage for our analysis, so we have to choose wisely.

The Breusch-Pagan test allows us to test for homoscedasticity. If the Breusch-Pagan test shows that there is conditional heteroskedasticity, one could use weighted least squares (if the source of heteroskedasticity is known) or use standard errors consistent with heteroskedasticity.

In my work on various projects, I've found that neglecting to validate the model's assumptions can lead to unreliable results. For example: I once overlooked multicollinearity among features, which led to inflated coefficients and poor generalization to new data. Now, I always check correlation matrices or use VIF scores. On another occasion, my model suffered from heteroscedasticity, causing unevenly distributed errors. A residual plot quickly caught this, and I had to transform my dependent variable to stabilize variance. In short, always double-check these key assumptions. If something's off, the diagnostic tools are your best friends for getting your model back on track.

Before obtaining the final result it is necessary to locate outliers and outliers. I recommend two techniques, in R Studio: - The z-value indicates the number of standard deviations a value has from the mean. - quartiles of the variable to calculate lower and upper bounds. In this way we will see if the extreme data distort our model.

Interpreting the model's output is where the rubber meets the road. Over the years, I've honed a routine: Early in my career, I used to focus solely on the size of the coefficients. I've since learned that understanding their signs (+/-) is equally important for gauging the direction of the effect. In a project involving customer behavior, ignoring high p-values led me to overestimate the impact of certain features. Now, I always consider the significance level to avoid spurious conclusions. These days, I give more weight to the adjusted R-squared as it accounts for model complexity.

The two main statistical means of validity testing: K-S Index and the Gini Index. - K-S = is the maximum separation between the good and the bad. K-S=100% is the perfect - Gini= is the area between the random and the satisfactory model. We cannot forget about the inference of deniers. They are analysed if there is a proportion equal to or greater than 5% and through overfitting, i.e. removing variables from the model from smallest to largest by analysing how many rejected become accepted by removing those variables.

Validation is the reality check for your model. I've found the following to be invaluable: On a healthcare project, skipping cross-validation led to a model that couldn't generalize well. Now, it's a standard step for me to ensure robustness. For quicker projects, I've used this simpler split cross validation check method. However, I always make sure the split is random to avoid bias. Once, residuals revealed a pattern I'd missed, indicating my model was incomplete. Diagnostic plots are now a must-do for me to assess model stability.

When using frequentist regression approaches it is important to not just fixate on the p-values of the model coefficients. Be sure to validate the stability of the model (distribution of residuals, number of coefficients, potential collinearity between coefficients). If the sole purpose of the model is to get high accuracy predictions, consider experimenting with a machine learning approach as well. The benefit of regression models are their interpretability and ease of use