STA215H5 Chapter Notes - Chapter 7: The Intercept, Standard Deviation, Dependent And Independent Variables
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7. 1 least squares: the line of best fit . The correlation says that the linear association between two variables can be strong, but it doesn"t tell you how to predict one variable from the other. A linear model gives an equation of a straight line through the data. No straight line can go through all the points, but a linear model can summarize the general pattern with only a couple of parameters. Like all models of the real world, the line will be wrong wrong in the sense that it can"t match reality exactly, but it can help us understand how the variables are associated. The line of best fit is the line for which the sum of the squared residuals is smallest, hence called the least squares line. In statistics, we use a slightly different model for the equation of a line:
