<< Statistics`LinearRegression`

This is Problem #5.25 in Levenspiel.

Clear[tau, cA, cA0, rate, recipRate, conc]

x[1] = 300;
y[1] =  0.65;
z[1] = 2.0;
x[2] = 240;
y[2] =  0.92;
z[2] = 2.0;
x[3] = 250;
y[3] =  1.0;
z[3] = 2.0;
x[4] = 110;
y[4] = 0.56;
z[4] = 1.0;
x[5] = 360;
y[5] =  0.37;
z[5] = 1.0;
x[6] = 24;
y[6] =  0.42;
z[6] = 0.48;
x[7] = 200;
y[7] =  0.28;
z[7] = 0.48;
x[8] = 560;
y[8] =  0.20;
z[8] = 0.48;

tau = Table[x[i], {i, 1, 8}]
cA = Table[y[i], {i, 1, 8}]
cA0 = Table[z[i], {i, 1, 8}]
recipRate = 
      Table[{y[i], x[i]/(z[i] - y[i])}, {i, 1, 8}] // N

cA0 = 0.8;
xA = 0.75;
cAf = cA0*(1 - xA);

dataPlot1 = 
        ListPlot[recipRate, PlotStyle -> PointSize[0.02], 
          AxesOrigin -> {0, 0}];
recipRateVsConc = 
      Regress[recipRate, Table[conc^i, {i, 0, 5}], conc, 
        RegressionReport -> RSquared]
fittedRecipRateVsConc = 
      Fit[recipRate, Table[conc^i, {i, 0, 5}], 
        conc]
Integrate[%, {conc, cAf, cA0}]

Plot[fittedRecipRateVsConc, {conc, 0.2, 0.8}, 
        AxesOrigin -> {0, 0}];

Show[%, dataPlot1];

Note that the result is (very?) sensitive to the goodness of the polynomial fit. Analyze how the calculated holding time (or space-time) varies for polynomials of order 3, 4 and 5. Which one conforms best to the experimental data points?