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For more than one explanatory variable, the process is called multiple linear regression.Most commonly, the conditional mean of y given the value of X is assumed to be an affine function of X; less commonly, the median or some other quantile of the conditional distribution of y given X is expressed as a linear function of X.Firstly, let’s consider the potential effect on the health of the prostate gland.

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The case of one explanatory variable is called simple linear regression.Thus, although the terms "least squares" and "linear model" are closely linked, they are not synonymous.In linear regression, the observations (red) are assumed to be the result of random deviations (green) from an underlying relationship (blue) between the dependent variable (y) and independent variable (x).This is because models which depend linearly on their unknown parameters are easier to fit than models which are non-linearly related to their parameters and because the statistical properties of the resulting estimators are easier to determine. Most applications fall into one of the following two broad categories: Linear regression models are often fitted using the least squares approach, but they may also be fitted in other ways, such as by minimizing the "lack of fit" in some other norm (as with least absolute deviations regression), or by minimizing a penalized version of the least squares loss function as in ridge regression (L-norm penalty).Conversely, the least squares approach can be used to fit models that are not linear models.

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