Basis
Functions

The Basics of Basis Functions

The Characteristics of Spline Functions

The Characteristics of Spline Functions II

Goods

Dissecting the U.S. Nondurable Goods Index

Smoothing the Nondurable Goods Index

Phase-Plane Plotting of the Goods Index

Growth

The Features of Human Growth Data

-Introduction
-Figure 1
-Figure 2
-Conclusion

From Raw Data to Functional Data

Smoothing the Growth Data

Monotone Smoothing of the Growth Data

Weather

Weather Introduction

Summarizing the Functional Data

Weather Data Analysis

The Features of Human Growth Data
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Expertise: Beginner

Figure 1 shows, for each of 10 girls, the height function H(t) as estimated from 31 observations taken between 1 and 18 years. Note that the times of measurement are not equally spaced. These data were collected as part of the Berkeley Growth Study. Growth is the most rapid in the earliest years, but we note the increase in slope during the pubertal growth spurt (PGS) that occurs at ages ranging from about 9 to 15 years. One girl is tall for all ages, but some girls can be tall during childhood, but end up with a comparatively small adult stature. The intervals between height measurements are six months or more, and the picture from this long-term perspective is of a relatively smooth growth process.

Figure 1: The heights of the first 10 females in the Berkeley Growth Study.
Circles indicate the ages at which measurements were taken.

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