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Understanding Scrubbiness in Linear Regression Models

Scrubbiness is a measure of how well a model is able to remove noise from the data. It is defined as the ratio of the variance of the residuals (the difference between the predicted values and the actual values) to the variance of the original data. A higher scrubbiness value indicates that the model is better at removing noise, while a lower scrubbiness value indicates that the model is more noisy.

In your case, you are using a linear regression model to predict the price of a house based on its features. The scrubbiness of the model can be calculated as follows:

Scrubbiness = (Variance of residuals) / (Variance of original data)

where the variance of the residuals is the average of the squared differences between the predicted prices and the actual prices, and the variance of the original data is the average of the squared differences between each feature and its mean value.

For example, if the variance of the residuals is 100 and the variance of the original data is 1000, then the scrubbiness of the model would be:

Scrubbiness = (100) / (1000) = 0.1

This means that the model is only able to remove 10% of the noise from the data, and there is still a lot of noise present in the predictions.

It's important to note that scrubbiness is not a measure of the accuracy of the model, but rather a measure of how well the model is able to remove noise from the data. A model with high accuracy may still have low scrubbiness if it is highly sensitive to noise in the data.

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