How do we use matrices to find estimates in Linear Models?

A 4 × 400 relay race is run as follows. There are four runners, each of whom runs 400 meters. The first runner carries a baton, which she passes to the second runner, etc. Each runner’s time is taken by a coach. The four coaches report times of 59.0, 61.0, 61.0, 59.0.

Suppose that another coach takes the time of the entire team, and he reports 4:01. Provide a point estimate together with a 95% confidence interval for the true time of runner

This would be a combination of random variables and we need to use expectation of a random matrix and covariance matrix to estimate the values(?)

  • $\begingroup$ In the last sentence, is it asking for a confidence interval for the true time of the entire team? $\endgroup$
    – angryavian
    Oct 4 '20 at 3:59
  • $\begingroup$ Yes I believe so. True time of the four runners. $\endgroup$
    – BVon
    Oct 4 '20 at 4:19

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