# How to predict from glm created with average values?

I want to predict count data (example: people visiting a beach) based on some predictors (example: temperature, cloudiness).

I have created a generalized linear model (with Poisson distribution and logarithmic link function) using historic data. The model consists of three coefficients: intercept $\beta_0$, temperature coefficient $\beta_T$ and cloudiness coefficient $\beta_C$. For given temperature $T$ and cloudiness $C$, the predicted number of people $X$ visiting the beach is then $$X(T,C)=\exp(\beta_0+\beta_T T+\beta_C C)$$

My question: When I use average values to calculate the model parameters (e.g. monthly mean values of $X$, $T$ and $C$), can I use the resulting parameters to predict daily values?

If not, is it possible when I train on other values, e.g. $\exp$ of the average of $\ln X$ instead of the average of $X$?

Transforming $X$ doesn't help. To make finer-grained predictions, you need finer-grained data.
• Thanks! Let's replace beachgoers with a physical variable that can in principle be modeled (e.g. leafs dropped from a tree), and assume that the log-linear relationship is physically sound (within some bounds, e.g. for a certain vegetation period, validated e.g. by a day-by-day count for a short duration). When I have a large number of observations, from my understanding it should be possible to show mathematically that the $\beta_i$ calculated from the averages of $\ln X$, $T$, $C$ are the same (or almost the same) as when calculated from the non-average observations. Any thoughts? May 30, 2016 at 7:00