从预测的非线性模型数据中插入曲线，需要方程 R

如何解决从预测的非线性模型数据中插入曲线，需要方程 R

我需要定义一个方程来表示模型中的一系列点。由于它们是已经拟合的非线性回归的预测，因此噪声应该不是问题。我看过很多允许对曲线进行预测的例子，但我仍然对如何从各种函数（如样条等）中检索方程感到困惑。

基于我为 brms 中的非线性回归提供的公式（b1^b2，其中 b1 ~ 1 + x 和 b2 ~ 1），我希望这种关系类似于某种幂函数 [ax^b 或可能(int + ax)^b]。

我知道这可能只是一个近似值 - 只要它相对相似就可以了（将与模型一起绘制以进行比较）。非常感谢任何见解，如果我能提供更多信息，请告诉我。已在下方提供示例数据。


x <- c(7,7.5,8,8.5,9,9.5,10,10.5,11,11.5,12,12.5,13,13.5,14,14.5,15,15.5,16,16.5,17,17.5,18,18.5,19,19.5,20,20.5,21,21.5,22,22.5,23,23.5,24,24.5,25,25.5,26,26.5,27,27.5,28,28.5,29,29.5,30,30.5,31,31.5,32,32.5,33,33.5,34,34.5,35,35.5,36,36.5,37,37.5,38,38.5,39,39.5,40,40.5,41,41.5,42,42.5,43,43.5,44,44.5,45,45.5,46,46.5,47,47.5,48,48.5,49,49.5,50,50.5,51,51.5,52,52.5,53,53.5,54,54.5,55,55.5,56,56.5,57,57.5,58,58.5,59,59.5,60,60.5,61)

y <- c(38.0136100143096,41.7377019494229,45.0570784133659,49.7413206704322,54.1226793545035,58.5143924911556,64.0149939443995,70.2996105120598,74.5157778956172,82.0845639640055,88.1447395709772,96.0901896008888,104.331306746698,112.587794035369,116.793284692497,129.660032344424,139.148796580701,154.021720779283,164.352212638548,174.265834929441,186.345636353806,199.537020067263,217.599140020487,233.877433057235,246.132735977878,267.47374365421,283.863259012889,301.899794004843,322.769938301311,351.430583957233,383.849198025211,390.736999633559,423.249193342341,454.638021905869,485.240521462023,509.31872397953,560.804077944124,580.52077607546,623.750134417424,663.267081364541,698.778452300861,737.091827116676,796.938400847035,856.419990917143,906.017778910945,965.168165262045,1013.84413110147,1065.85753522486,1154.33958805326,1204.13058748532,1322.42312105971,1385.41472565674,1464.95636449756,1526.04430007742,1609.84006688626,1738.45992222218,1816.05261609804,1896.50702990984,2024.59349402727,2142.55345863206,2216.16848789472,2384.32905391336,2534.20713772314,2599.97048189298,2800.82684813604,2956.9306593113,3133.9558188069,3320.82577045419,3477.57994233654,3602.69160098815,3800.51701252841,4062.6001499355,4238.73826354165,4645.61124406474,4731.78190196944,4947.75977778357,5211.86923419648,5619.65143369664,5817.33879970144,6079.00167282099,6205.39929607976,6681.42573862285,7198.53801041513,7267.01092369979,7816.95660375773,8133.793609116,8261.13289172042,9053.74531584895,9473.33768555856,10137.0504777871,10400.797014819,10966.3727089692,11494.3384956937,11920.4271066324,12400.9643350626,13096.7674700334,13798.7159321491,14358.3675127649,15266.2675882016,16072.0949530508,17058.7362901159,17663.6886724086,18390.5282871649,19307.9213621373,20392.6725381775,21431.4257870743,21624.312458088,23099.2069971926,24090.3844352512)

data <- data.frame(x,y)


library(ggplot2)

ggplot(data,aes(x,y)) + geom_point()

编辑：回复@Bernhard

是的，我尝试使用这些输出，但没有发现它们能很好地近似曲线 - 也许我误解了如何使用它们。

如果我的 brms 输出如下所示：

 Family: lognormal 
  Links: mu = identity; sigma = identity 
Formula: weight.g ~ b1^b2 
         b1 ~ 1 + dia.1.cm
         b2 ~ 1
   Data: CaesCombBot.data.wfrag (Number of observations: 2619) 
Samples: 4 chains,each with iter = 5000; warmup = 2000; thin = 5;
         total post-warmup samples = 2400

Population-Level Effects: 
             Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
b1_Intercept     6.61      0.81     5.08     8.24 1.00     1741     1787
b1_dia.1.cm      0.98      0.42     0.42     2.07 1.00     1738     1974
b2_Intercept     0.57      0.06     0.46     0.70 1.00     1727     1942

Family Specific Parameters: 
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.56      0.01     0.54     0.57 1.00     2156     2105

Samples were drawn using sampling(NUTS). For each parameter,Bulk_ESS
and Tail_ESS are effective sample size measures,and Rhat is the potential
scale reduction factor on split chains (at convergence,Rhat = 1).

我如何使用它来重新创建等式？

例如当我尝试时

curve((6.61 + 0.98*x)^0.57,from = 0,to = 50)

只是做一个快速比较：x 值 40 (6.61 + 0.98*40)^0.57 = exp(8.846) [以对数正态分布建模] = 6946.547

我知道它看起来不一样（因为它也在对数正态分布中），但希望 exp 值与下图相匹配？（根据add_predictions，x值为40对应5256.29）