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FIGURE 19-12: You can adjust the smoothness of the fitted curve by adjusting the smoothing fraction.

Looking at Figure 19-12, you can observe the following:

Setting

produces a rather stiff curve that rises steadily between ages 2 and 40, and then

declines steadily after that (see dashed line). The value 0.667 represents 2/3, which is what R uses

as the default value of the f parameter if you don’t specify it. This curve misses important features

of the data, like the low pre-puberty hormone levels, the flat plateau during child-bearing years,

and the slowing down of the yearly decrease above age 65. You can say that this curve shows

excessive bias, systematically departing from observed values in various places along its length.

Setting

, which is at a lower extreme, produces a very jittery curve with a lot of up-and-

down wiggles that can’t possibly relate to actual ages, but instead reflect random fluctuations in the

data (see dark, solid line). You can say that this curve shows excessive variance, with too many

random fluctuations along its length.

Setting

produces a curve that’s stiff enough not to have random wiggles (see medium, solid

line). Yet, the curve is flexible enough to show that hormone levels are fairly low until age 10,

reach their peak at age 20, stay fairly level until age 50, and then decline, with the rate of decline

slowing down after age 70. This curve appears to strike a good balance, with low bias and low

variance.

Whenever you do LOWESS regression, you have to explore different smoothing fractions to