A Breeder of Thoroughbred Horses Wishes to Model the Relationship

question 74

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. $\begin{array}{cccccc}\text { Horse } & \text { Gestation } & \text { Life } & \text { Horse } & \text { Gestation } & \text { Life } \\& \text { period } & \text { Length } & & \text { period } & \text { Length } \\& x \text { (days) } & y \text { (years) } & & x \text { (days) } & y \text { (years) } \\1 & 416 & 24 & 5 & 356 & 22 \\2 & 279 & 25.5 & 6 & 403 & 23.5 \\3 & 298 & 20 & 7 & 265 & 21 \\4 & 307 & 21.5 & & &\end{array}$
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 $\hat { y } = 18.89 + .01087 x$ .

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Definitions:

Sequencer File

A file or data structure used in programming PLCs (Programmable Logic Controllers) to manage a sequence of operations or instructions.

Shift Registers

Digital circuits that shift the data stored within them by one position either to the right or left when a control signal is applied.

Control Processes

Methods and procedures used to monitor, adjust, and manage the operation of systems or processes to achieve desired outcomes, emphasizing regulation and manipulation of variables.

Destination

The end point or target location to which data, signals, or physical items are directed in a system or process.