A residual is the difference between the real value for our target variable and the predicted value. There are several methods for this, the most common of which is called Residual Sum of Squares (RSS).
For each data point, we want to measure how far from our prediction the actual data was. This is where the concept of error or “residuals” comes into play. But given some data, how can we create a such a model it? There are an infinite number of lines to choose from, so which is the best? We need a way to measure how good our model is. Our estimate for the target variable is expressed as a bias term or intercept plus a weighted sum of our input variables. So, for the time being, let us return from the vast jungles of machine learning to the tamed and comfortable community of traditional statistical models, the first of which will be linear regression. Likewise, an economist may be more concerned with understanding the general relationship between political uncertainty in elections, uncertainty in public policy, and uncertainty in financial markets, than creating a complex interactive system that prevents generalizations that could be applied to governance, electioneering, or market trading. If they create a neural network to do this, we may have low error in the system but our human understanding of the laws of nature is no better. Additionally, it is often the case that we want to understand our models or have some measures of how valid they are.įor example, the goal of a physicist may be to understand their model of a particle interaction. While they have great capacity and are sometimes the only solution to difficult problems, their downsides can be substantial depending on what our goals are. Machine Learning models are big, complicated, and almost impossible to interpret.
Before we get into talking about linear regression, you may recall that we recently have discussed advanced machine learning techniques such as neural networks and support vector machines, but these are not always the most appropriate tool for modeling data.
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