![]() ![]() If we represent the total number of weights and features as w(n)x(n), then we could represent the formula like this:Īfter establishing the formula for linear regression, the machine learning model will use different values for the weights, drawing different lines of fit. In other words, while the equation for regular linear regression is y(x) = w0 + w1 * x, the equation for multiple linear regression would be y(x) = w0 + w1x1 plus the weights and inputs for the various features. In the case of “ multiple linear regression”, the equation is extended by the number of variables found within the dataset. However, a regression can also be done with multiple features. The process described above applies to simple linear regression, or regression on datasets where there is only a single feature/independent variable. Photo: Cbaf via Wikimedia Commons, Public Domain () The parameters of the model are adjusted during training to get the best-fit regression line. ![]() So the equation is read as: “The function that gives Y, depending on X, is equal to the parameters of the model multiplied by the features”. In the above equation, y is the target variable while “w” is the model’s parameters and the input is “x”. Machine learning practitioners represent the famous slope-line equation a little differently, using this equation instead: Meanwhile, m is the slope of the line, as defined by the “rise” over the “run”. X refers to the dependent variable while Y is the independent variable. Lines are typically represented by the equation: Y = m*X + b. The goal is to find an optimal “regression line”, or the line/function that best fits the data. The line represents the function that best describes the relationship between X and Y (for example, for every time X increases by 3, Y increases by 2). The relationship between the input variables (X) and the target variables (Y) can be portrayed by drawing a line through the points in the graph. In linear regression, it’s assumed that Y can be calculated from some combination of the input variables. The function of a regression model is to determine a linear function between the X and Y variables that best describes the relationship between the two variables. If we had the amount of memory on the X-axis and the cost on the Y-axis, a line capturing the relationship between the X and Y variables would start in the lower-left corner and run to the upper right. The exact memory-to-cost ratio might vary between manufacturers and models of hard drive, but in general, the trend of the data is one that starts in the bottom left (where hard drives are both cheaper and have smaller capacity) and moves to the upper right (where the drives are more expensive and have higher capacity). If we plotted out the individual data points on a scatter plot, we might get a graph that looks something like this: ![]() The more memory we purchase for a computer, the more the cost of the purchase goes up. Let’s suppose that the dataset we have is comprised of two different features: the amount of memory and cost. Understanding Linear RegressionĪssume that we have a dataset covering hard-drive sizes and the cost of those hard drives. That was a quick explanation of linear regression, but let’s make sure we come to a better understanding of linear regression by looking at an example of it and examining the formula that it uses. In linear regression tasks, every observation/instance is comprised of both the dependent variable value and the independent variable value. The dependent variable is the variable that is being studied, and it is what the regression model solves for/attempts to predict. As the independent variable is adjusted, the levels of the dependent variable will fluctuate. The independent variable is the variable that stands by itself, not impacted by the other variable. In linear regression tasks, there are two kinds of variables being examined: the dependent variable and the independent variable. Linear regression is an algorithm used to predict, or visualize, a relationship between two different features/variables. ![]()
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