Reading through your explanation of a little analyze regression, it seems like we can use multicollinearity to our advantage sometimes. I mean that knowing that two variables are dependent on one another can actually be a useful tool in understanding the model. I'm thinking for example if you see that there is a high correlation between amount of time browsed and items purchased, you then know to try to keep people browsing for longer periods.

My post was:

Multicollinearity is problem that you can run into when you're fitting a regression model, or other linear model. It refers to predictors that are correlated with other predictors in the model. Unfortunately, the effects of multicollinearity can feel murky and intangible, which makes it unclear whether it's important to fix.

The two types are:

Structural multicollinearity: This type occurs when we create a model term using other terms. In other words, it's a byproduct of the model that we specify rather than being present in the data itself. For example, if you square term X to model curvature, clearly there is a correlation between X and X2.

Data multicollinearity: This type of multicollinearity is present in the data itself rather than being an artifact of our model. Observational experiments are more likely to exhibit this kind of multicollinearity.

Multicollinearity occurs when independent variables in a regression model are correlated. This correlation is a problem because independent variables should be independent. If the degree of correlation between variables is high enough, it can cause problems when you fit the model and interpret the results. In regression, "multicollinearity" refers to predictors that are correlated with other predictors. Multicollinearity occurs when your model includes multiple factors that are correlated not just to your response variable, but also to each other. In other words, it results when you have factors that are a bit redundant.

An easy way to detect multicollinearity is to calculate correlation coefficients for all pairs of predictor variables. If the correlation coefficient, r, is exactly +1 or -1, this is called perfect multicollinearity. If r is close to or exactly -1 or +1, one of the variables should be removed from the model if at all possible.

The Consequences of Multicollinearity

1. Imperfect multicollinearity does not violate Assumption 6. Therefore the Gauss Markov Theorem tells us that the OLS estimators are BLUE.

2. The variances and the standard errors of the regression coefficient estimates will increase. This means lower t-statistics.

3. The overall fit of the regression equation will be largely unaffected by multicollinearity. This also means that forecasting and prediction will be largely unaffected.

4. Regression coefficients will be sensitive to specifications. Regression coefficients can change substantially when variables are added or dropped.

Step-by-step explanation

A little Analyze regression coefficients

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Multicollinearity

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A Lot Do not analyze Regression Coefficients

With this in mind, the analysis of regression coefficients should be contingent on the extent of multicollinearity. This means that the analysis of regression coefficients should be preceded by an analysis of multicollinearity. If the set of independent variables is characterized by a little bit of multicollinearity, the analysis of regression coefficients should be straightforward. If there is a lot of multicollinearities, the analysis will be hard to interpret and can be skipped.

If two or more independent variables have an exact linear relationship between them then we have perfect multicollinearity.

Examples: including the same information twice (weight in pounds and weight in kilograms), not using dummy variables correctly (falling into the dummy variable trap), etc.