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I'm searching for a regression model (preferably in R) that can fit data with two variables of which the dependent variable has an upper limit. The data is of the kind "temperature of a glass of cold water over time". Here, we would have time and temperature as variables where temperature increases slower and slower as the water approaches the temperature of its surroundings.

To be more specific about the actual data: It consists of two columns, one is of the format "Date" ("YYYY-MM-DD") and the other one is an integer, the "NDVI". The NDVI is an index to estimate the vegetation cover of an area. After a wildfire, it is reduced and will recover until reaching a max value. For each point in time, there are about 5000 observations of the NDVI value. It is unknown how low the initial NDVI value actually is, but the max value can be estimated.

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There are many models that can likely fit the data you've described; however, without a more thorough description of your data, it will be impossible for anyone here to make specific recommendations.

Under the assumption that you data consist of two columns only (a time of the measurements and a value of the measurement), it sounds like your observations will likely fail to be independent of one another (e.g., knowing one temperature value helps you make a better guess what the value of the next measurement will be), which is an important requirement of classical regression models.

It sounds like you may be interested in some sort of autoregressive model, which can have some properties such as stationarity which, at first glance, seem like they might be analogous to the issue you described (e.g., the system returns to a certain mean value after time has passed with no additional "shocks" (e.g., changes in temp introduced to the system).

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