<< Graphics`Graphics`
<< Statistics`LinearRegression`

data = 
        List[{100, 0}, {90, 1}, {80, 4}, {70, 9}, {60, 16}, {50, 25}, {40, 
            35}, {30, 45}, {20, 55}, {10, 64}, {0, 71}];
dataPlot = 
        ListPlot[data, 
          PlotStyle -> PointSize[0.02]];
cRfit = 
      Regress[data, Table[cA^i, {i, 0, 4}], cA, 
        RegressionReport -> RSquared]
cR = Fit[data, Table[cA^i, {i, 0, 4}], cA]
Plot[%, {cA, 5, 95}];

phiCorrect = -D[cR, cA]
phiWrongData = 
      List[{90, 0.10}, {80, 0.20}, {70, 0.30}, {60, 0.40}, {50, 0.50}, {40, 
          0.58}, {30, 0.64}, {20, 0.69}, {10, 
          0.72}]
ListPlot[phiWrongData, PlotStyle -> PointSize[0.02], 
        PlotRange -> {0, 1}, 
        AxesOrigin -> {0, 0}];
phiWrongFit = 
      Regress[phiWrongData, Table[cA^i, {i, 0, 4}], cA, 
        RegressionReport -> RSquared]
phiWrong = 
      Fit[phiWrongData, Table[cA^i, {i, 0, 4}], 
        cA]
Plot[{phiCorrect, phiWrong}, {cA, 5, 98}];

cA01 = 100;
cA02 = 70;
cAf = 10;

phiPFR1c = (1/(cA01 - cAf))*
          Integrate[phiCorrect, {cA, cAf, cA01}] // 
        N
phiPFR2c = (1/(cA02 - cAf))*
          Integrate[phiCorrect, {cA, cAf, cA02}] // 
        N
cRfPFR1c = (cA01 - cAf)*phiPFR1c
cRfPFR2c = (cA02 - cAf)*phiPFR2c
phiNewC = phiCorrect /. cA -> 10
cRfMFR1c = phiNewC*(cA01 - cAf)
cRfMFR2c = phiNewC*(cA02 - cAf)

phiPFR1w = (1/(cA01 - cAf))*
          Integrate[phiWrong, {cA, cAf, cA01}] // 
        N
phiPFR2w = (1/(cA02 - cAf))*
          Integrate[phiWrong, {cA, cAf, cA02}] // 
        N
cRfPFR1w = (cA01 - cAf)*phiPFR1w
cRfPFR2w = (cA02 - cAf)*phiPFR2w
phiNewW = phiWrong /. cA -> 10
cRfMFR1w = phiNewW*(cA01 - cAf)
cRfMFR2w = phiNewW*(cA02 - cAf)