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### multicollinearity in OLS regression [duplicate]

If I have a dependent variable Y and two independent variables X1 and X2 , that are highly correlated. Y ~ beta1*X1 + beta2*X2 What issues can multicollinearity cause in an OLS regression, apart ...
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### What correlation makes a matrix singular and what are implications of singularity or near-singularity?

I am doing some calculations on different matrices (mainly in logistic regression) and I commonly get the error "Matrix is singular", where I have to go back and remove the correlated variables. My ...
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### Regression coefficients that flip sign after including other predictors

Imagine You run a linear regression with four numeric predictors (IV1, ..., IV4) When only IV1 is included as a predictor the standardised beta is +.20 When you ...
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### How problematic is it to control for non-independent covariates in an observational (i.e., non-randomized) study?

Miller and Chapman (2001) argue that it is absolutely inappropriate to control for non-independent covariates that are related to both the independent and dependent variables in an observational (non-...
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### Is centering a valid solution for multicollinearity?

Let's assume that $y = a + a_1x_1 + a_2x_2 + a_3x_3 + e$ where $x_1$ and $x_2$ both are indexes both range from $0-10$ where $0$ is the minimum and $10$ is the maximum. I found by applying VIF, CI and ...
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### Testing difference between two (adjusted) r^2

Let's say I have two regression models, one with three variables and one with four. Each spits out an adjusted r^2, which I can compare directly. Obviously, the model with the higher adjusted r^2 is ...
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### Relationship Between Correlation and Multicollinearity [duplicate]

Suppose I've a model such as $Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \cdots + \beta_k X_k + \epsilon$. Now, there's high correlation between $X_1$ & $X_2$ (say over 60% but below 75%). Does ...
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### Modeling prices with the Hedonic regression

I'm using the concept of Hedonic regression in order to model the prices for real estates. I'm having some trouble with my approach. What I have and what I do my data consists out of real estates ...
871 views

### Fitting linear model through noisy data

I'm currently working on a predictive modeling project. I have to predict $Y$ given variables $X_1,X_2,X_3$ and $X_4$ that are not necessarily independent. Our first idea was to propose a linear ...
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### Abusing Linear Models under Multicollinearity: Simulation for 'realistic' movement of predictors

I have a reasonable understanding of why multicollinearity is a problem is regression models, along the lines of this excellent post. To summarise my understanding, for a regression model of \$y = \...