如何为数据集找到 model

Question

I have a text file that contains dates and numerical values like

1.1.2020, 45.67
2.1.2020, 49.65
4.1.2020, 47.58
31.1.2020, 55.88
...

Note that value of some dates is missing.

I would like to fit a model of the form ae^(bx) to find an estimate what would be value in 1.1.2021. How can I do that? Is there some Sagemath function for that or some Python library to find such a model.

Answer 1

For your specified formula, this can be solved by fitting a log-log model.

Y = a * exp(b x)
log(Y) = log(a) + b x

1. Transform your dates into numeric type (for ex. as.numeric() )
2. Fit an ordinary linear model
3. Back transform the results onto the original scale

Y = exp(intercept + slope*date)

In R, using some made up data

dates=sort(sample(1:100,20))
values=exp(seq(0,5,length.out=20))+rnorm(20)

mod=lm(log(values)~dates)

new=1:100
plot(values~dates)
points(exp(coef(mod)[1]+coef(mod)[2]*new)~new,col="red")