A Breeder of Thoroughbred Horses Wishes to Model the Relationship

Essay

A breeder of Thoroughbred horses wishes to model the relationship between the gestation period and the length of life of a horse. The breeder believes that the two variables may follow a linear trend. The information in the table was supplied to the breeder from various thoroughbred stables across the state. $\begin{array}{cccccc}\begin{array}{cccc}\text { Horse }\end{array} & \begin{array}{c}\text { Gestation } \\\text { period }\\x \text { (days) } \end{array} & \begin{array}{c}\text { Life } \\\text { Length }\\ y \text { (years) } \end{array} & \text { Horse } & \begin{array}{c}\text { Gestation } \\\text { period } \\x \text { (days) } \end{array} & \begin{array}{c}\text { Life } \\\text { Length }\\ y \text { (years) } \end{array} \\1 & 416 & 24 & 5 & 356 & 22 \\2 & 279 & 25.5 & 6 & 403 & 23.5 \\3 & 298 & 20 & 7 & 265 & 21 \\4 & 307 & 21.5 & & &\end{array}$

Summary statistics yield $S S _ { x x } = 21,752 , S S _ { x y } = 236.5 , S S _ { y y } = 22 , \bar { x } = 332$ , and $\bar { y } = 22.5$ . Find a $95 \%$ prediction interval for the length of life of a horse that had a gestation period of 300 days. Use $s = 2$ as an estimate of $\sigma$ and use $y = 18.89 + .01087 x$