Construct a Confidence Interval About the Slope of the Least $90 \%$

Short Answer

Construct a Confidence Interval about the Slope of the Least -squares Regression Model
-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. Construct a $90 \%$ confidence interval about the slope of the true least-squares regression line.
$\begin{array} { c c c c c c } \text { Horse } & \text { Gestation } & \text { Life } & \text { Horse } & \text { Gestation } & \text { Life } \\ & \begin{array} { c } \text { period } \\ x \text { (days) } \end{array} & \begin{array} { c } \text { Length } \\ \text { y (years) } \end{array} & & \text { period } & \text { Length } \\ 1 & 416 & 24 & 5 & \text { x (days) } & \text { y (years) } \\ 2 & 279 & 25.5 & 6 & 403 & 22 \\ 3 & 298 & 20 & 7 & 265 & 21 \\ 4 & 307 & 21.5 & & & \end{array}$