I have the following dataset:
> df1 Location SalesQty product 1 location 3 1 prod1 2 location 3 0 prod1 3 location 3 3 prod1 4 location 5 3 prod1 5 location 5 0 prod1 6 location 5 4 prod1 7 location 3 2 prod2 8 location 3 5 prod2 9 location 5 2 prod2 10 location 5 1 prod2
I want to perform a poisson regression to predict/estimate the SalesQty of prod1 on location 3 and 5 and prod 2 on location 3 and 5 (I know there are not enough datapoints such that a predictor will be significant). The SalesQties can be visualised as:
If you run:
Reg <- glm(SalesQty ~ Location, family = "poisson", data = df1)
The predictions on each location is just the average per location. This is due to the least squares error per location.
If you run:
Reg <- glm(SalesQty ~ product + Location, family = "poisson", data = df1)
I am figuring out how the coefficients of each categorized predictor play a role in the formula for predicting the SalesQty of a product on a location.
Only considering the location, the formula will be: ln(SalesQty) = $\beta_0$ + $\beta_5 I_5$ with $\beta_0$ beiing the intercept corresponding to location 3. Now $exp(\beta_0)$ is the average of the SalesQties of location 3 and $exp(\beta_0$ + $\beta_5)$ is the average of the SalesQties of location 5. But when considering 2 categorical predictors, the location ánd the product, I don't see how to interpret the coeficients and the modelling formula.
I hope someone can send me in the right direction