data lntrans;
title 'CHATTERJI & PRICE PAGE 36 - VIOLATION OF LINEARITY';
input bacteria time;
lnbac=log(bacteria);
cards;
355 01
211 02
197 03
166 04
142 05
106 06
104 07
060 08
056 09
038 10
036 11
032 12
021 13
019 14
015 15
;
proc chart;
  vbar bacteria;
  vbar lnbac;
proc plot;
  plot bacteria*time='*';
  plot lnbac*time='*';
proc reg;
  model bacteria = time;
  model lnbac = time;
run;
  


CHATTERJI & PRICE PAGE 36 - VIOLATION OF LINEARITY                             

Frequency

8 +       *****
  |       *****
  |       *****
  |       *****
  |       *****
7 +       *****
  |       *****
  |       *****
  |       *****
  |       *****
6 +       *****
  |       *****
  |       *****
  |       *****
  |       *****
5 +       *****
  |       *****
  |       *****
  |       *****
  |       *****
4 +       *****
  |       *****
  |       *****
  |       *****
  |       *****
3 +       *****       *****       *****
  |       *****       *****       *****
  |       *****       *****       *****
  |       *****       *****       *****
  |       *****       *****       *****
2 +       *****       *****       *****
  |       *****       *****       *****
  |       *****       *****       *****
  |       *****       *****       *****
  |       *****       *****       *****
1 +       *****       *****       *****                   *****
  |       *****       *****       *****                   *****
  |       *****       *****       *****                   *****
  |       *****       *****       *****                   *****
  |       *****       *****       *****                   *****
  --------------------------------------------------------------------
            40         120         200         280         360

                            BACTERIA Midpoint


Frequency

4 +                                                  *****
  |                                                  *****
  |                                                  *****
  |                                                  *****
  |                                                  *****
  |                                                  *****
  |                                                  *****
  |                                                  *****
  |                                                  *****
  |                                                  *****
3 +                 *****      *****                 *****
  |                 *****      *****                 *****
  |                 *****      *****                 *****
  |                 *****      *****                 *****
  |                 *****      *****                 *****
  |                 *****      *****                 *****
  |                 *****      *****                 *****
  |                 *****      *****                 *****
  |                 *****      *****                 *****
  |                 *****      *****                 *****
2 +      *****      *****      *****      *****      *****
  |      *****      *****      *****      *****      *****
  |      *****      *****      *****      *****      *****
  |      *****      *****      *****      *****      *****
  |      *****      *****      *****      *****      *****
  |      *****      *****      *****      *****      *****
  |      *****      *****      *****      *****      *****
  |      *****      *****      *****      *****      *****
  |      *****      *****      *****      *****      *****
  |      *****      *****      *****      *****      *****
1 +      *****      *****      *****      *****      *****      *****
  |      *****      *****      *****      *****      *****      *****
  |      *****      *****      *****      *****      *****      *****
  |      *****      *****      *****      *****      *****      *****
  |      *****      *****      *****      *****      *****      *****
  |      *****      *****      *****      *****      *****      *****
  |      *****      *****      *****      *****      *****      *****
  |      *****      *****      *****      *****      *****      *****
  |      *****      *****      *****      *****      *****      *****
  |      *****      *****      *****      *****      *****      *****
  -------------------------------------------------------------------------
          2.7        3.3        3.9        4.5        5.1        5.7

                                LNBAC Midpoint


                  Plot of BACTERIA*TIME.  Symbol used is '*'.

         400 +
             |
             |
             |
             |
             |  *
         350 +
             |
             |
             |
             |
             |
         300 +
             |
             |
    BACTERIA |
             |
             |
         250 +
             |
             |
             |
             |
             |      *
         200 +          *
             |
             |
             |
             |              *
             |
         150 +
             |                  *
             |
             |
             |
             |                      *
         100 +                          *
             |
             |
             |
             |
             |                              *   *
          50 +
             |                                      *
             |                                          *   *
             |                                                  *
             |                                                      *   *
             |
           0 +
             ---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+--
                1   2   3   4   5   6   7   8   9  10  11  12  13  14  15

                                          TIME



                    Plot of LNBAC*TIME.  Symbol used is '*'.

LNBAC |
      |
  6.0 +
      |
      | *
      |
      |
      |
  5.5 +
      |
      |      *
      |           *
      |
      |                *
  5.0 +
      |                     *
      |
      |
      |                          *    *
      |
  4.5 +
      |
      |
      |
      |
      |                                    *
  4.0 +                                         *
      |
      |
      |
      |                                              *
      |                                                   *
  3.5 +                                                        *
      |
      |
      |
      |
      |                                                             *
  3.0 +
      |                                                                  *
      |
      |
      |                                                                       *
      |
  2.5 +
      |
      --+----+----+----+----+----+----+----+----+----+----+----+----+----+----+-
        1    2    3    4    5    6    7    8    9   10   11   12   13   14   15

                                         TIME



Model: MODEL1
Dependent Variable: BACTERIA

Analysis of Variance

                         Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F
Model            1 106080.35714 106080.35714       60.619       0.0001
Error           13  22749.37619   1749.95201
C Total         14 128829.73333

    Root MSE      41.83243     R-square       0.8234
    Dep Mean     103.86667     Adj R-sq       0.8098
    C.V.          40.27512

Parameter Estimates

                 Parameter      Standard    T for H0:
Variable  DF      Estimate         Error   Parameter=0    Prob > |T|
INTERCEP   1    259.580952   22.72999119        11.420        0.0001
TIME       1    -19.464286    2.49996572        -7.786        0.0001

 
Model: MODEL2
Dependent Variable: LNBAC

Analysis of Variance

                         Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F
Model            1     13.35869     13.35869     1103.702       0.0001
Error           13      0.15735      0.01210
C Total         14     13.51603

    Root MSE       0.11002     R-square       0.9884
    Dep Mean       4.22576     Adj R-sq       0.9875
    C.V.           2.60346

Parameter Estimates

                 Parameter      Standard    T for H0:
Variable  DF      Estimate         Error   Parameter=0    Prob > |T|
INTERCEP   1      5.973160    0.05977810        99.922        0.0001
TIME       1     -0.218425    0.00657471       -33.222        0.0001