I have an indicator from a data set, described by a variable (e.g. Y). based on the general understanding, Y is affected by two possible factors, for example, factor a and factor b. however, i do not know the exact influence. in addition, it is not possible for me to do an orthogonal experiment to test.
at the same time, I have another indicator (e.g. Z) from data set Z, Y and Z are very similar indicators sharing same physical meaning, and Y and Z are assumed to be comparable (or very similar). the key is: we know that Z is only affected by factor a ( which means factor b does not exist with z).
my question is: is there any statistical method can be used to project the influence of factor a on Z to Y, in order to separate the influence of b on Y? (maybe assuming that the influence of a on Z is equivalent to its influence on Y)
I would like to explain the question with the following example:
Suppose I have sample data of "travel speed" on roads over city A for a specific time period. for example, we sample travel speed data on 1000 roads(randomly chosen) in city A during 9:00 am - 10:00 am (only make 1 sample for each road in this hour for one day, randomly), the observation lasts for 31 days (one month, from 1st to 31st). in addition, we have the similar sample for City B. the general idea is, we want to measure the traffic service level by calculating the probabilities of "facing low travel speed on road" in the sample data set (let's call it "jam risk"). as we know, because the general traffic demand changes with the day of week, the jam risk also changes with day of week. for example, it is more likely to suffer from traffic jam on Monday than on Wednesday in urban area. therefore, if we make a linear regression between day of week and jam risk and check the variance explained. we will find the relation. this is what we find in city A. however, in city B, except for the day of week, we can find another factor which is considered to influence the jam risk. for example, in city B, there is a "travel restriction" policy, which means for each day of a week, there are one group of cars are not allowed to run in the city. if you own a city in such city B, you can only drive it for 6 days. generally, the policy maker will try their best to make the number of banned cars for each day to be similar ( this is to say, there are about 1/7 cars are banned, but not sure) . my question is, is there any useful statistical method for me to analyse the influence of "restriction group policy" on the jam risk ( have to separate the influence of day of week) ? my idea is maybe it is possible to project the influence of day of week in city A to city B by some method, but how?