MATH 11 Lecture Notes - Lecture 5: Duodecimal, Interpolation
Document Summary
Since correlations are involved, we need our three conditions from before. There should not be a pattern in your residual plot. If you calculate the correlation from the old faithful example, you get r=0. 854. For a give linear model, r^2=r^2 is the proportion of the variation in the y-variable that is accounted for (or explained) by the variation in the x-variable. So, r^2 = 0. 854^2=0. 73= 73% of how long we must wait is completely determined by how long the last eruption lasted. As another example, the r^2 in the height-weight regression is 0. 67 so 67% of the variability in weights is simply because of height differences. Often, you can identify subgroups in your original data or in the residuals. In this case, split your data into different parts and do several linear regression instead of one, clunky, regression. Subgroups can be explained by different outside causes.
