I have a dataset that has high collinearity among variables. When I created the linear regression model, I could not include more than five variables ( I eliminated the feature whenever VIF>5). But I need to have all the variables in the model and find their relative importance. Is there any way around it?. I was thinking about doing PCA and creating models on principal components. Does it help?.

I am currently trying to figure out whether my data (consisting of thousands of rows, some is numerical, and some are categorical, and some are ordinal) has multicollinearities or not. One thing I have noticed is that my data is not normally distributed, based on the Shapiro-Wilk test. As is the case with mostly (if not all) real world data, as answered here But based on several posts, including this one, many suggests the ANOVA (Categorical vs Numerical) or the …

I know that multicolinear predictors in a model aren't ideal because it causes the model to be sensitive to very minor changes, which then reduces our ability to interpret the effects of each predictor from its coefficient. However, I don't understand why the model becomes sensitive and how the estimated coefficients can vary wildly from just a very minor change in the dataset. Also, does multicolinear predictors affect the accuracy / error on a prediction? Or does it purely affect …

At my office, I am stuck in a weird situation. I am asked to perform a regression algorithm on the data, in which the target variable is continuous having values range between 0.6 to 0.9 with 8 digits of precision after the decimal. Although I know and have applied many linear and non-linear regression algorithms in the past the case here is something different. There is one variable, which, according to my BU, should have a positive and linear correlation …

Let’s suppose that the stock value of various companies is the target of my models. I have some “internal” predictors e.g. yearly sales of each company, sum of salaries at each company etc. I have some “external” predictors e.g. geographical position of each company (latitude & longitude), population in the area in which each company operates etc. Therefore, each observation at my dataset is about the stock value of a company along with its internal and external predictors. The purpose …

Based on my model, if I decline someone due to their score, it should be able to provide some reasoning as to which variables mainly contributed to the decision to decline. Typically in Logistic Regression models, this is a simple exercise where you calculate (Beta * X) for each variable and pick 1 or 2 variables which caused the biggest score drop. However, this isn't very straightforward for non-linear models. I would appreciate any ideas on handling something like this. …

I am working on a model where the underlying data is inherently correlated by groups. So some of my observations are almost duplicates but not quite. The problem is pretty simple, I have a y variable to predict from a discrete x variable and several other potential predictor variables which may or may not be significant. The observations are not quite independent, they're taken from groups of underlying events but I want to handle this better. I could approach the …

Can someone explain to me like I'm five on why multicollinearity does not affect neural networks? I've done some research and neural networks are basically linear functions being stacked with activation functions in between, now if the original input variables are highly correlated, doesn't that mean multicollinearity happens?

One of the assumptions for Linear regression is no multicollinearity. Why does the regression model don't intelligently assign a zero coefficient to one of the correlated variables?

I have been working through the derivation of the formula used to calculate the Variance Inflation Factor associated with a model. I am hoping to start with the Least Squares equation as defined in matrix form and find a proof that derives this, linked here: derivation of VIF I understand correlation is equal to cov/ $\hat{\sigma}^2$ and $VIF_{j}$ is the jth predictor is jth diagonal entry of inverse of correlation matrix. But how is this related to $VIF_{j}=\frac{Var({\hat{\beta_j}})}{\sigma^2}$ ? I'd …

I have been trying to understand how multicollinearity within the independent variables would affect the Linear regression model. Wikipedia page suggests that only when there is a "perfect" multicollinearity, one of the independent variables would have to be removed from training. Now my question is that should we only remove one of the columns if the correlation is equal to +/- 1 or do we consider a threshold (say 0.90) after which it should be considered as perfect multicollinearity.

I have been taught to check correlation matrix before going for any algorithm. I have a few questions around the same: Pearson Correlation is for numerical variables only. What if we have to check the correlation between a continuous and categorical variable? I read some answer where Peter Flom mentioned that there can be scenarios where correlation is not significant but two variables can be multi-collinear? Removing the variable is the only solution? I was asked in an interview if …

I am doing an exercise of a Machine Learning System module in python that takes a dataset of cars (cylinders, year, consumption....) and asks for a model, being the variable to predict the consumption of gasoline. As it has three categorical variables, I have generated the dummies. In the exercise I need to eliminate the variables with multicollinearity, so I used the method showed on my course notes: from sklearn.linear_model import LinearRegression def calculateVIF(data): features = list(data.columns) num_features = len(features) …

I am working on a linear model with 6 independent variables and when thinking about including an interaction I got lost. An interaction exists if the level of one independent variable is affected by another independent variable. Doesn't that therefore mean that if an interaction exists there may also be collinearity problems? Similarly, if the correlation is low between the two variables, then that should imply there is no interaction? I hope my question makes sense and that someone can …

While I am aware that tree-based algorithms (e.g., DT, RF, XGBoost) are 'immune' to multi-collinearity, how do they handle linearly combined features? For example, is there is any additional value or harm in including the three feature: a, b and a+b in the model?

While there may not be any added value in standardizing one-hot encoded features prior to applying linear models, is there is any harm in doing so (i.e., affecting model performance)? Standardizing definition: applying (x - mean) / std to make the feature mean and std 0, 1 respectively) I prefer applying standardization to my entire training dataset after one-hot encoding, rather than applying it only to the numerical features. I feel it would significantly simplify my pipeline. For example, if …

From various books and blog posts, I understood that the Variance Inflation Factor (VIF) is used to calculate collinearity. They say that VIF till 10 is good. But I have a question. As we can see in the below output, the rad feature has the highest VIF and the norm is that VIF till 10 is okay. How does VIF calculate collinearity when we are passing an entire linear fit to the function? And how to interpret the results given …

I've read that multicollinearity is one of the main assumptions of multivariate linear regression - Multicollinearity occurs when the independent variables are too highly correlated with each other. However, when learning linear regression, one of the key topics is the idea of introducing interaction terms into the model to model the interaction effect which is when the effect of an independent variable on a dependent variable changes, depending on the value(s) of one or more other independent variables. Aren't these …

I have a medical dataset with features age, bmi, sex, gender, # of children, region, charges, smoker. Here smoker, gender, sex and region are categorical variables and others are numerical features. How do I check for collinearity between these in my dataset?

I'm a beginner in Machine learning and I've studied that collinearity among the predictor variables of a model is a huge problem since it can lead to unpredictable model behaviour and a large error. But, are there some models (say GLM) that are perhaps 'okay' with collinearity unlike the classic linear regression? It is said that the classic linear regression assumes there is no correlation between its independent variables. This question arises because I was doing a project that said …