The linear regression model
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It is time for the actual introduction of regressions! Let's start with some dry theory. A linear regression is a linear approximation of a causal relationship between two or more variables. Regressions models are highly valuable as they are one of the most common ways to make inferences and predictions. The process goes like this: you get sample data, come up with a model that explains the data and then make predictions for the whole population based on the model you have developed. There is a dependent variable labeled Y being predicted and an independent variable labeled x1 x2 and so forth these are the predictors Y is a function of the X variables and the regression model is a linear approximation of this function. The easiest regression model is the simple linear regression y is equal to beta 0 plus beta 1 times X plus Epsilon. Let's see what these values mean. Y is the variable we are trying to predict and is called the dependent. Variable X is the independent variable. When using regression analysis we want to predict the value of y provided. We have the value of x but to have a regression Y must depend on X in some causal way. Whenever there is a change in X such change must translate into a change in Y.
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