Images as Matrices Explained: The Math Behind Computer Vision

If "investment in newspaper ads" doesn’t contribute much to sales, while "radio" has an average contribution and "tv" has a high contribution, you might see the following in terms of multicollinearity:

1. **Low Contribution Variables**: If "newspaper" ads don't affect sales much, and its correlation with "radio" or "tv" is low, it might not significantly impact multicollinearity. However, if it's highly correlated with "radio" or "tv," it could still introduce some multicollinearity.

2. **High Contribution Variables**: For "radio" and "tv," if they have a strong impact on sales and are highly correlated with each other, multicollinearity could be a concern. This means it might be hard to separate their individual effects on sales.

**In Practice**:

- **Check Correlations**: Look at how "newspaper," "radio," and "tv" are correlated with each other. High correlations suggest multicollinearity.

- **Assess Impact**: Even if "newspaper" doesn’t contribute much to sales, if it's highly correlated with the other predictors, it might still affect the model's performance.

- **Consider Adjustments**: If multicollinearity is present, you might need to adjust your model by removing one of the correlated predictors or combining them in some way.

In summary, even if some variables don't seem to contribute much, their relationships with other predictors can still affect the analysis due to multicollinearity.

What Is Multicollinearity in Regression? A Beginner’s Guide

Multicollinearity occurs when two or more predictor variables in a regression model are highly correlated, meaning they provide similar information about the response variable. This can make it difficult to determine the individual effect of each predictor on the outcome.

### Simple Example

Let's say you want to predict someone's **weight** based on their **height** and **shoe size**.

- **Height** and **shoe size** are often correlated because taller people generally have larger feet.

- In this case, both height and shoe size might explain some of the variation in weight, but because they are correlated, it’s hard to figure out how much of the variation in weight is due to height and how much is due to shoe size. 

### Why It’s a Problem

When multicollinearity is present:

1. **Coefficient Estimates Become Unreliable**: The estimates of the coefficients for height and shoe size could become very large or even have unexpected signs (like a positive relationship showing up as negative).

2. **Statistical Significance**: It might appear that neither height nor shoe size is statistically significant, even though together they should explain weight well.

### How to Spot It

One way to spot multicollinearity is by looking at the **correlation** between the predictors. If height and shoe size have a high correlation (close to 1 or -1), there might be multicollinearity.

### Simplified Visualization

- Imagine a Venn diagram with two overlapping circles, one for height and one for shoe size. The overlapping part represents the shared information. Multicollinearity means there's a large overlap, making it hard to separate the individual contributions of height and shoe size to the prediction of weight.

In summary, multicollinearity makes it difficult to distinguish the separate effects of highly correlated variables on the outcome, leading to unstable estimates and potential misinterpretation of the model.