The following examples will investigate meteorological normalization in settings violating the assumptions of Proposition 2 the prediction models, while γ is some offset. For example, Y could indicate the concentration of a pollutant that is increasing linearly in time T (α > 0) and that is affected by precipitation X, which is a binary variable (e.g., rain/no rain). Specifically, we assume that precipitation (X = 1) reduces the pollutant concentration by a value of β > 0 due to "washing out". We further assume that the probability of precipitation depends on the time T . Specifically, we assume that