Least absolute deviation regression, also known as L1 regression, is a type of regression analysis that minimizes the absolute difference between the observed values and the predicted values. This approach is useful in situations where there are outliers in the data, as it is less sensitive to the effects of these outliers compared to other regression methods such as least squares regression.

One example of L1 regression is in the analysis of housing prices. In this scenario, a real estate agent may have a dataset of 100 houses, with their corresponding prices and square footage. Using L1 regression, the agent can predict the price of a new house based on its square footage, while minimizing the absolute deviation between the predicted and observed prices. This approach can help the agent to more accurately predict the price of a house, even if there are some outliers in the dataset (e.g. a house that is significantly over or underpriced compared to the others).

Another example of L1 regression is in the analysis of stock prices. In this scenario, an investor may have a dataset of daily stock prices for a particular company over a period of time. Using L1 regression, the investor can predict the future stock price based on historical data, while minimizing the absolute deviation between the predicted and observed prices. This approach can help the investor to make more informed decisions about when to buy or sell the stock, even if there are some outliers in the dataset (e.g. a sudden market crash or spike).

Overall, L1 regression is a useful tool for dealing with outliers in regression analysis. By minimizing the absolute deviation between the predicted and observed values, L1 regression can provide more accurate predictions and insights compared to other regression methods.