Multiple variables Bootstrap Example 1: Estimate of regression parameters

The variables X and Y conform to a simple least squares regression model if the underlying probabilistic relationship between these two variables is of the form:

Y = Normal(mX+c,s)

This is a parametric model for which we try to determine the parameters m, c, s from the observations.

Note: if both X and Y are Normally distributed (i.e. X,Y is bivariate Normal) then the above relationship always holds, and

where r is the correlation coefficient.

We will look at two approaches to estimating these parameters using the Bootstrap:

Parametric Bootstrap

Non-parametric Bootstrap

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