# How to bootstrap samples from data that has more than dependent variable?

I understand bootstrap sampling with replacement. But what i still not sure about is that how to apply this approach to sample from data that has more than one dependent variables.

For example, suppose my data collected from different routes in a small city, x= distance (in km) and y=time (in minutes) as:

Distance(x)    Time(y)
12             15
2              5
4              4
..              ..


Now to apply bootstrap, i cannot deal with x and y separately,obliviously, as the time depend on the distance and nature of route. I was thinking to do either:

1- add a new column (z), where z= time/distance,, then in my bootstrap i pick up a random x and z; and from that i can calculate y= x * z.

2- i pick up a random row (x and y), e.g., (12,15),((4,4),(4,4). So dealing with x and y as a single variable.

In the first solution, it gives me more combination, but may generate new data. In the second, it is only generating from the data i have.

My question is what out of these is the correct way to sample from my data.

• What parameter(s) do you seek to estimate by bootstrapping? – BruceET Jun 30 at 19:53
• i would like to simulate routes, so estimating x and y. in other words, in my simulation i wish to generate route data (x,y) -> then i do my calculation etc. – MWH Jun 30 at 20:08