Plot Practice, Illustrated by
GROWTH   OF   TORONTO   MALES 
                            G R O W T H
   175+
      -                                                   x   x
      -                                               x
H     -                                           x
E     -
I  150+                                       x
G     -                                   x
H     -                               x
T     -                           x
      -                       x
c  125+                   x
m     -               x
      -           x                         H = 80.3 + 5.16 A
      -       x
      -   x                                 S = 1.25
   100+
        --+---------+---------+---------+---------+---------+----
         5.0       7.5      10.0      12.5      15.0      17.5
                                   AGE years

QUESTIONS

With a ruler, draw a line by eye, then compare it to the line of the formula.

How much do these boys grow in one year? In ten years?

Obtain a growth rate from -
    1. The formula for the line
    2. The extreme points of the graph What are the units of the growth rate?

The growth plot is nearly linear. Would this linearity to extend to, say, age 30? If it did, how tall would be a 30 year old?

How far is a typical point from the line? Find the number that describes this.

Beside the height scale, now in cm., write a height scale in inches.
(If you carry no calculator, use 1 cm = 0.4 inches.)

Convert the formula,

H (in cm) = 80.3 + 5.16 Age
now in centimeters and years, to inches and years. Expanding the above to include bandwith,
H (in cm) = 80.3 + 5.16 Age ± 1.25 ,
Convert this to inches and years.

Do you think the points of the plot represent individual boys, or averages of many boys of the same age? 

                          R E S I D U A L S
       -
       -                                           o   o
       -
 R  1.5+
 E     -
 S     -                                                   o
 I     -
 D     -       o   o   o   o
 U  0.0+                       o               o
 A     -   o
 L     -
       -                           o
 c     -
 m -1.5+                               o   o
       -
       -                                                       o
         --+---------+---------+---------+---------+---------+----
         5.0       7.5      10.0      12.5      15.0      17.5
                                AGE years
Compare linearity of growth as seen
      1. On the growth plot
      2. On the residual plot

Find the "adolescent growth spurt" on the residual plot. (A residual plot acts as a microscope, magnifying small deviations about the line.)

On the residual plot, mark off horizontal lines at ±s = ±1.25.

  1. Are many of the residuals within this band?
  2. (Most of the residuals are within a band twice as broad.)
Source:
The data for these plots is taken from page 90 of
"On Growth and Form"   by Darcy Wentworth Thompson (Macmillan 1942)
where it is attributed to Boaz
William   Knight