214 LINEAR REGRESSION AND CORRELATION Ch. 7 



When this change in s Y is made in formula 7.37 we obtain the formula 

 for Sy which is employed in the following £-ratio: 



Y — Uvxi 



(7.38a) t = ^A 



where \i y . Xi = the true F-value for the ith. individual for whom X = X{. 

 Formula 7.38a and the usual methods make it possible to obtain a 

 confidence interval on fx y . Xi with any specified confidence coefficient. 

 It should be both clear and reasonable that such a confidence interval 

 will be longer than a corresponding one from formula 7.38 because the 

 standard deviation is larger. 



Problem 7.31. You are about to buy one turkey which weighs 6.5 pounds at 

 16 weeks of age, and you are going to keep it until it is at least 28 weeks of age. 

 What is the 94 per cent confidence interval on its 28-week weight, assuming it 

 comes from the population sampled in Table 7.22? 



It was seen in the discussion of Table 7.22 that Y = 0.6072X + 

 10.04, which = 13.99 pounds for X = 6.5 pounds. Also, s y . x = 0.679 

 pound, and 2(x 2 ) = 37.9120; hence by formula 7.39, after taking the 

 square root, 



s Y = 0.679Vl + 1/30 + (6.5-7.56)737.9120 = 0.700 



is the standard deviation of Y f or X = 6.5 pounds at 16 weeks of age. 

 Therefore, t = (13.99 — ii y . Xl )/0.700, and the 94 per cent confidence 

 interval is derived from 



-2.19(0.700) < (13.99 - ,*„.*.■) < 2.19(0.700). 



It is found that 



CI 94 is 12.5 < /x y . Xi < 15.5, 



to the nearest one-half pound. 



Notice that the situation just considered clearly is one in which 

 the confidence interval for a particular turkey is required. You do 

 not have a group of turkeys so that the high 28-week weights of some 

 of them can be expected to offset the low 28-week weights of others. 

 Therefore, you must face the fact that this particular turkey's weight 

 at 28 weeks of age may be quite low, as well as quite high, for turkeys 

 weighing 6.5 pounds at 16 weeks of age. 



Problem 7.32. Suppose that problem 7.31 is changed to state that you have 

 bought a rather large flock of 6.5-pound turkeys each 16 weeks of age. Compute 

 the CI 94 appropriate to this new situation. 



