/*
Berkeley Guidance Study.  Source: Weisberg

The data for this example are excerpted from the Berkeley Guidance Study,
a longitudinal monitoring of boys and girls born in Berkeley, California,
between January 1928 and June 1929. The variables included in the data are:

CaseNO   Case Number

WT2      weight at age 2 (kg).

HT2      height at age 2 (cm).

WT9      weight at age 9.

HT9      height at age 9.

LG9      leg circumference at age 9 (cm).

ST9      composite measure of strength at age 9 (high values=stronger)

WT18     weight at age 18.

HT18     height at age 18. LG18=leg circumference at age 18.

LG9      leg circumference at age 9 (cm).

ST18     strength at age 18.

SOMA     somatotype, a seven-point scale, as a measure of fatness
         (1 = slender, 7 = fat), determined using a photograph taken at age 18. 

GENDER   0=Boys 1=girls


Data for 26 boys and for 32 girls are given in file.
(complete study had larger n and more variables;
cf Tuddenham and Snyder, 1954, for details).

QUESTIONS

2.1.1   For the girls, obtain the matrix of sample correlations,
        the sample averages, and the sample standard deviations.

2.1.2   Fit the model

          SOMA = b0 + b1 HT2 + b2 WT2 + b3 HT9 + b4 WT9 + b5 ST9 + e

        Find sigma-hat, r-squared, the overall analysis of variance
        and F-test, and state the conclusion for the F-test.
        Compute t-statistics to be used to test each of the bj in
        the model equal to zero. Explicitly state the hypothesis
        tested by each and the conclusion. 

2.1.3   Now fit the model

          SOMA = b0 + b3 HT9 + b4 WT9 + b5 ST9 + e
          
        and compare this model to that fit in 2.1.2
        (i.e., compute an F-test)

2.1.4   Repeat 2.1.1 to 2.1.3, except for the boys.
        Qualitatively describe the difference between the fitted models
        for boys and for girls (formal procedures will be studied
        in Chapter 7).

2.1.5   For the boys, repeat the derivation in Section 2.1 when
        adding the variable WT9 to the model
          
          HTl8 = b0 + b2 WT2
          
          
Excerpts from data...

ID  WT2 HT2  WT9   HT9  LG9 ST9 WT18  HT18 LG18 ST18 SOMA G

201 13.6 90.2 41.5 139.4 31.6 74 110.2 179.0 44.1 226 7.0 0
202 12.7 91.4 31.0 144.3 26.0 73  79.4 195.1 36.1 252 4.0 0
203 12.6 86.4 30.1 136.5 26.6 64  76.3 183.7 36.9 216 6.0 0
...

227 11.5 89.7 29.0 138.6 24.6 61  67.7 180.7 34.3 164 4.0 0
228 14.2 92.2 31.4 140.0 28.2 74  68.5 178.7 37.0 219 2.0 0
...

331 12.6 83.8 33.0 136.5 29.0  57 71.2 169.6 38.8 107 6.0 1
334 12.0 86.2 34.2 137.0 27.3  44 58.2 166.8 34.3 130 5.0 1
...

383 13.3 86.4 41.4 138.2 32.5  44 82.8 162.8 42.5 125 7.0 1
384 13.2 94.0 41.6 142.0 31.0  56 68.1 168.6 38.4 142 5.5 1
385 15.9 89.2 42.4 140.8 32.6  74 63.1 169.2 37.9 142 5.5 1

*/

OPTIONS LS=75 PS=60;

DATA a;

  INFILE 'berkeley_data.txt' ;
  
  INPUT  CaseNo WT2 HT2 WT9 HT9 LG9 ST9 WT18 HT18 LG18 ST18 SOMA GENDER;
  
RUN;
  
/*
PROC SORT; BY GENDER;

PROC MEANS; BY GENDER; 

PROC REG; by Gender;
  Model WT18=HT18;

RUN;
*/