A Breeder of Thoroughbred Horses Wishes to Model the Relationship

question 76

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 $y = 18.89 + .01087 x$

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Definitions:

Spinal Motor Neurons

Nerve cells located in the spinal cord that initiate and control movements of the muscles.

Amyotrophic Lateral Sclerosis

A progressive neurodegenerative disease affecting nerve cells in the brain and spinal cord, leading to loss of muscle control and mobility.

General Weakness

A symptom characterized by a reduced strength in one or more muscles, not necessarily linked to any specific disease or disorder.

Throat

The front part of the neck, or the passage behind the mouth and nose that leads to the esophagus and larynx, essential for breathing, swallowing, and speaking.