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![]() However, because we tend to start by fitting the simplest relationship, many linear models are represented by straight lines. Note that the linear in linear model does not imply a straight-line relationship but rather that the response is a linear (additive) combination of the effects of the explanatory variables. In standard linear regression this is assumed to be a normal (Gaussian) distribution. ![]() The error term is drawn from a statistical distribution that captures the random variability in the response. It is inclusion of the error term, also called the stochastic part of the model, that makes the model statistical rather than mathematical. ![]() Where \(\alpha\) is the intercept (value of \(y\) when \(x\) = 0), \(\beta\) is the slope (amount of change in \(y\) for each unit of \(x\)), and \(\varepsilon\) is the error term. In simple linear regression, with a single explanatory variable, the model takes the form: For example, we could use linear regression to test whether temperature (the explanatory variable) is a good predictor of plant height (the response variable). It is used to model the relationship between a response (also called dependent) variable \(y\) and one or more explanatory (also called independent or predictor) variables \(x_\). Linear regression is the one of the most widely used statistical techniques in the life and earth sciences. One Continuous and One Categorical Variable ![]()
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