Our error metrics will be able to judge the differences between prediction and actual values, but we cannot know how much the error has contributed to the discrepancy. This term represents error that comes from sources out of our control, causing the data to deviate slightly from their true position. One of the reasons for this is the ϵ (named “epsilon”) term. Unless our data is a perfectly straight line, our model will not precisely hit all of our data points. As we’ll see, these outputs won’t always be perfect. Given the coefficients, if we plug in values for the inputs, the linear regression will give us an estimate for what the output should be. We will not delve into how these coefficients are calculated, but know that there exists a method to calculate the optimal coefficients, given which inputs we want to use to predict the output. The first coefficient without an input is called the intercept, and it adjusts what the model predicts when all your inputs are 0. What adjusts how strong the relationship is and what the direction of this relationship is between the inputs and outputs are our coefficients. The higher the inputs are, the higher (or lower, if the relationship was negative) the outputs are. Taken together, a linear regression creates a model that assumes a linear relationship between the inputs and outputs. In particular, regression deals with the modelling of continuous values (think: numbers) as opposed to discrete states (think: categories). Regression here simply refers to the act of estimating the relationship between our inputs and outputs. The regression part of linear regression does not refer to some return to a lesser state. If you’ve ever heard of “practice makes perfect,” then you know that more practice means better skills there is some linear relationship between practice and perfection. The linear part of linear regression refers to the fact that a linear regression model is described mathematically in the form: If that looks too mathematical, take solace in that linear thinking is particularly intuitive. Simply speaking, models are just functions where the outputs are some function of the inputs. Inputs can also be called independent variables or predictors, while outputs are also known as responses or dependent variables. These inputs and outputs have many names that you may have heard before. Models will look at other aspects of the data called inputs that we believe to affect the outputs, and use them to generate estimated outputs. In general, these models deal with prediction and estimation of values of interest in our data called outputs. In the context of regression, models refer to mathematical equations used to describe the relationship between two variables. If you’d like a quick refresher on the linear regression, you can consult this fantastic blog post or the Linear Regression Wiki page. The intuition behind many of the metrics we’ll cover here extend to other types of models and their respective metrics. The linear regression is the most commonly used model in research and business and is the simplest to understand, so it makes sense to start developing your intuition on how they are assessed. There are many types of regression, but this article will focus exclusively on metrics related to the linear regression. This article will dive into four common regression metrics and discuss their use cases. These metrics are short and useful summaries of the quality of our data. The quality of a regression model is how well its predictions match up against actual values, but how do we actually evaluate quality? Luckily, smart statisticians have developed error metrics to judge the quality of a model and enable us to compare regresssions against other regressions with different parameters. We can plug our data back into our regression equation to see if the predicted output matches corresponding observed value seen in the data. But this ease can cause us to forget to evaluate our regressions to ensure that they are a sufficient enough representation of our data. When you learn Python or R, you gain the ability to create regressions in single lines of code without having to deal with the underlying mathematical theory. Regressions are one of the most commonly used tools in a data scientist’s kit. But how do we precisely describe this relationship to other people? How can we describe how strong this relationship is? Luckily, we can describe relationships between phenomena, such as practice and skill, in terms of formal mathematical estimations called regressions. For example, we observe that if we practice our programming everyday, our related skills grow. Human brains are built to recognize patterns in the world around us.
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