Breeding of thoroughbreds. The breeding ability of a thoroughbred horse is sometimes a more important consideration to prospective buyers than racing ability. Usually, the longer a horse lives, the greater its value for breeding purposes. Before marketing a group of horses, a breeder would like to be able to predict their life spans. The breeder believes that the gestation period of a thoroughbred horse may be an indicator of its life span. The information in the next table was supplied to the breeder by various stables in the area. (Note that the horse has the greatest variation of gestation period of any species due to seasonal and feed factors.) Consider the first-order model
y = β0 + β1x + ε.
where y = life span (in years) and x = gestation period (in months).
(a) Fit the model to the data.
(b) Check model adequacy by interpreting the F and R2 statistics.
(c) Construct a plot of the residuals versus x, gestation period.
(d) Check for residuals that lie outside the interval 0 ± 2s or 0 ± 3s.
(e) The breeder has been informed that the short life span of horse #3 (7 years) was due to a very rare disease. Omit the data for horse #3 and refit the least squares line. Has the omission of this observation improved the model?