204: Height and Weight of School Children in Glasgoiv 
TABLE I. 
Glasgow. 
Age 
Group ,1, Boys 
Group B, Boys 
Group (7, Boys 
Group D, Boys 
6" 
IF= 
-21-164 + 1-5030 
ir= 
-22-576 + 1-5320 
IF= 
- 24-489 + 1-5910 
IF= 
- 25-678 + 1-6030 
7 
- 21 -065 + 1-5] 9 fl' 
TF= 
-26 -308 + 1-6350 
1F= 
- 27-390 + 1-6670 
\V= 
- 34-819 + 1-8180" 
8 
ll' = 
- 19-381+1 -495^7 
Tl^= 
-28-127 + 1-6950 
W= 
- 6-640 + 1-2270 
IF= 
- 32 777 + 1790// 
9 
1F= 
- 24-652 + r635/r 
ir= 
-32-826 + 1-8180 
1F= 
- 20-671 + 1-5620 
IF= 
- 36-030 + 1-8830" 
10 
)F= 
-29-589 + r768iy 
Tr= 
-35-696+1-8990 
TF= 
- 42-942 + 2-0550 
TF= 
- 51-636 + 2-2180 
11 
)r= 
-54-9iO + 2-3O20 
ir= 
-39-725 + 2-0050 
]F= 
- 43-628 + 2-0880 
1F= 
- 67 -664 + 2 •5460' 
12 
-49-513 + 2-217Z? 
TF= 
-62-890 + 2-4760 
IF= 
- 55-386 + 2-3370 
TF= 
- 62-052 + 2-4500 
13 
lf= 
-65-467 + 2-5470 
w= 
-63-516 + 2-5110 
W= 
- 81-342 + 2-8540 
W= 
- 99 -908 + 3- 1600 
lit 
1F= 
-83-784 + 2-8880 
)F= 
- 76-749 + 2-7750' 
W= 
- 103-661 +3-25U/ 
\V= 
-126-446 + 3-6330 
Age 
Group A, Girls 
Group B, Girls 
Group C, Girls 
Group D, Girls 
6 
TF= - 14-561 + 1-3290 
W= 
-15-985 + 1-3450 
IF= 
- 23-728 + 1-5510 
IF= 
- 27-563 + 1-6240" 
7 
1F= -19-762 + 1-465 0 
W = 
-24-130+1-5560 
rF= 
- 29-312+1-6930 
TF= 
- 30-226 + 1-6940 
8 
JF= - 20-721 +1-503//" 
TF= 
-30-622 + 1-718// 
TF= 
- 29-113 + 1-6910 
TF= 
- 40-156 + 1-9270" 
9 
If = -30-133+1-7300 
TF= 
-29-081 + 1-7090 
W= 
- 38-624 + 1-9170" 
IF= 
- 45-066 + 2-0450 
10 
TF= -36-478+1-8780 
1F= 
-38-866 + 1-9250 
1F= 
- 46-263 + 2-0880 
W= 
- 62-015 + 2-3970" 
11 
IF= -48-707 + 2-1530" 
TF= 
-43-005+2-0340 
IF= 
- 51-146 + 2-2090^ 
TF= 
- 57-754 + 2-3390 
13 
. 1F= -58-277 + 2-3600 
TF= 
-63-908 + 2-465// 
W= 
- 77-316+2-7350 
TF= 
- 84-298 + 2-8590 
13 
Tf = -74-156 + 2-6940" 
IF= 
-88-043 + 2-9390 
TF= 
- 83-960 + 2-8920 
1F= 
-103-594 + 3-229/r 
U 
IF= -95-464 + 3-0840 
IF= 
-84-496 + 2-9060 
TF= 
-106-133 + 3-3170 
TF.- 
-134-197 + 3-8040 
TF is weight in lbs., 
// is 
height in inches. 
The ages are centml ages, and to obtain the weight corresponding to a given height 
the child should be taken to the nearest whole year. 
weight on age and not height on age which is non-linear. The departure from 
linearity is not great, but Mr H. E. Soper, in order to smooth the material, fitted a 
parabolic surface to the regression surface of weight on height and age. 
Let TF be as before the weight in lbs., i/'^- height in inches, and y equal the 
age of the child measured from 10*. Then 
is the form of the surface when the relation of ^¥ to H for a given age is sensibly 
linear. 
Mr Soper now assumed : 
01 ill) = «o + + a./if, 0, {]]) = h, + h^xj + b,f 
and determined and a^, b„, and b.,, so that: 
2 {w (01 (?/) - Wo - «i 1/ + (hy'')] = m inim u m , 
t {n (0., iy) -bo- b^y - b.jf)} = minimum, 
where n. is the number of individuals in any age group. 
* Thus y takes every value from - 4 to +4 and we have nine equations to deal with. 
