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