Consider the model function
$${\displaystyle y=\alpha +\beta x,}$$
which describes a line with slope β and y-intercept α. In … See more

Description of the statistical properties of estimators from the simple linear regression estimates requires the use of a statistical model. The following is based on assuming the validity … See more

In SLR, there is an underlying assumption that only the dependent variable contains measurement error; if the explanatory variable is also … See more

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Relationship with the sample covariance matrix
The solution can be reformulated using elements of the covariance matrix: $${\displaystyle {\widehat {\beta }}={\frac {s_{x,y}}{s_{x}^{2}}}=r_{xy}{\frac {s_{y}}{s_{x}}}}$$ See more

This data set gives average masses for women as a function of their height in a sample of American women of age 30–39. Although the OLS article argues that it would be more appropriate to run a quadratic regression for this data, the simple linear … See more

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