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