Say you have data as shown below and the data represents Incidents of a certain type at a Toll Plaza.
The incident count is directly related to the Vehicles Per Day (VPD), so you can calculate the Incident Rate = Incident Count / VPD. Columns P1,P2 and P3 are predictor variables representing for example P1 = Distance from nearest town, P2 = Width of Area, etc. Scatterplots indicate that variables P1, P2 and P3 are related to the Incident Rate, but there is a lot of noise in the data. Each observation is taken over the same conditions/time and I have about 3,000 observations.
The client is considering to invest funds to improve equipment so that P3 will be reduced. They want to make a statement such as: "If we improve P3 by X% then the incident count will reduce by Y%". Of course, it can be qualified by, for example, specifying the conditions of P1 and P2 under which this will be true.
My question: (a) I am thinking of using R's GLM and do a Poisson Regression - is this the right approach to enable me to see if I make a statement like the above? and (b) If so, how would you approach this once you have the model output - would you use the model coefficients, P-values or look at relative importance of predictors using e.g. the relaimpo library , or would you rather make predictions with the model and analyse the model outcomes to get the impact of changing P3?