我需要找出适应某种疾病每天被污染的功率曲线方程，以便做出预测，数据如下：
Day Contaminated
26/feb 1
29/feb 2
04/mar 3
05/mar 8
06/mar 13
07/mar 19
08/mar 25
10/mar 34
11/mar 52
12/mar 81
13/mar 98
14/mar 121
15/mar 176
16/mar 234
17/mar 291
18/mar 428
19/mar 621
20/mar 904
21/mar 1128
22/mar 1546
23/mar 1891
24/mar 2201
25/mar 2433
我相信我需要在R中进行幂曲线回归（NonLinearRegression），但是我不知道如何实现它。
这是使用data.table，ggplot2和nls的方法。
首先，让我们将日期固定为标准格式并转换为整数，以便进行一些计算。
library(data.table)
library(ggplot2)
setDT(data)
data[,Day:= as.Date(Day,"%d/%b")]
data[,Int := as.integer(Day)-min(as.integer(Day))]
然后，我们使用nls将模型拟合到数据中。我们将使用公式y = a * x ^ b。
nls(formula = Contaminated ~ a * Int ^ b,data,start=list(a=1,b=1))
# Nonlinear regression model
# model: Contaminated ~ a * Int^b
# data: data
# a b
#2.272e-05 5.571e+00
# residual sum-of-squares: 123279
#
#Number of iterations to convergence: 48
#Achieved convergence tolerance: 7.832e-07
现在，我们可以使用ggplot查看结果。
ggplot(data,aes(x=Int,y=Contaminated)) +
geom_point() +
scale_x_continuous(breaks = c(0,10,20),labels = data$Day[data$Int %in% c(0,20)]) + xlab("Date") +
geom_smooth(method="nls",formula = y ~ a * x ^ b,method.args = list(start = c(a=1,b=1)),se=FALSE,linetype = 1)
数据
data <- structure(list(Day = c("26/feb","29/feb","04/mar","05/mar","06/mar","07/mar","08/mar","10/mar","11/mar","12/mar","13/mar","14/mar","15/mar","16/mar","17/mar","18/mar","19/mar","20/mar","21/mar","22/mar","23/mar","24/mar","25/mar"),Contaminated = c(1L,2L,3L,8L,13L,19L,25L,34L,52L,81L,98L,121L,176L,234L,291L,428L,621L,904L,1128L,1546L,1891L,2201L,2433L)),class = "data.frame",row.names = c(NA,-23L))