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I used the package library(respirometry) where I then calculated a Q10 value and an exponential Q10 function. My data describes reaction rates (y-axis) and temperature (x-axis)

R_vec<-c(59.30417,25.17243,52.66955,43.12963,145.29852,193.97691,236.89912,210.35885,320.23098,191.12217,147.24903,48.89208,32.88568,42.43895,112.43556,138.64379,251.85190,311.22275 ,305.99481,204.57434,110.43752,27.86627,25.55593,44.73207,56.92945,111.58071,308.65409,207.8143,229.17585,233.12221,103.07271,38.26464,69.34925,199.72791,255.01797,188.30957,181.65170,69.06965,47.91171,47.33007,77.23250,215.56555,222.82550,199.22744,125.79686,62.54028,56.56693,83.46246,248.88899,97.51262,32.85744,190.31608,235.28843,227.93966 ,179.88509,69.64359,43.01391,86.14514,235.26539,202.96242,178.81976,147.50266,57.77056,48.64468)
T_vec<-c(2.80,8.10,12.60,7.40,16.10,20.50,20.40,18.40,25.80,14.80,13.00,5.30,9.40,6.80,15.20,14.30,22.40,23.70,20.80,16.50,7.40,4.61,4.79,8.30,12.10,18.40,22.00,14.60,15.40,15.50,8.20,10.20,14.80,23.40,20.90,14.50,13.00,9.00,2.00,11.60,13.00,21.00,24.70,22.30,10.80,13.20,9.70,15.60,21.00,10.60,8.30,20.70,24.30,17.90,14.70,5.50,7.20,11.70,22.30,17.80,15.50,14.80,2.10,7.30)

Using the Q10 function I calculated an exponential function

 best_fit = Q10(R_vec = R_vec, T_vec = T_vec, model = TRUE)$model
    summary(best_fit)

In the literature a Q10 function is always validated with an R^2. As an R^2 cannot be applied to nonlinear functions, I tried to linearize following equation that I obtained from the summary() function: R_vec = 39.853860* exp(0.081536*T_vec)

lm <- lm(R_vec ~ log(39.853860*exp(0.081536*T_vec)))
summary(lm)
plot(lm)

This gives me an R^2 but not the one describing this exact function above, rather the best fitting exponential model. What am I missing in order to obtain the R^2 for my specific function generated with the Q10 function?

Cyril
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    As suggested by [this answer](https://stackoverflow.com/questions/14530770/calculating-r2-for-a-nonlinear-least-squares-fit), there are a bunch of different "pseudo" R^2 values defined for nonlinear fits. Do you know which ones people usually use in the literature? (I would say that the title of your question should probably be "how do I get an R^2 value value for a nonlinear fit?", as that's your real goal ... – Ben Bolker Nov 01 '20 at 16:22
  • Thank you @BenBolker Bolker. I adjusted the question. I don't know which R^2 they used. Which one would you suggest in the case of my data? – Cyril Nov 02 '20 at 13:25

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