The article referred to in Exercise 23 presents values for the dependent and independent variables for 10 additional construction jobs. These values are presented in Tables SE24A and SE24B (page 661).

a. Using the equation constructed in part (a) of Exercise 23, predict the concrete quantity (y) for each of these 10 jobs.

b. Denoting the predicted values by ŷ₁, . . . ,ŷ₁₀ and the observed values by ŷ₁, . . . ,ŷ₁₀, compute the quantities ŷ_i ?? ŷ_i . These are the prediction errors.

c. Now compute the fitted values ŷ₁, . . . , ŷ₂₈ from the data in Exercise 23. Using the observed values y₁, . . . , y₂₈ from those data, compute the residuals y_i ?? ŷ_i .

d. On the whole, which are larger, the residuals or the prediction errors? Why will this be true in general?

TABLE SE24A Data for Exercise 24

TABLE SE24B Data for Exercise 24

y X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 27.0 1,713 344 3,400 1,616 2,240 5,700 9,125 11,980 6,390 2,656 2,943 3,340 170 4.2 4.0 1 179 4,200 2,255 2,396 12,284 15,435 8,064 11,364 5,592 2,943 6,000 4,980 2,672 3,259 9,864 8,140 8,156 10,486 5,696 3,540 6,293 700.0 15.1 42 101 140 3 3.4 20.0 1 5.0 5.0 133 751.5 16.7 30 474 3 3.4 28.0 1 116 798.8 17.0 24 1,336 1,916 1,280 1,683 901 190 15 7.0 26.0 3.5 1 344 818.9 16.0 86 365 18 5.6 26.5 3.5 2 307 852.5 12.4 68 599 2.1 28.3 4.0 1 283 896.0 14.0 68 213 12 7.9 29.0 3.5 1 361 947.0 13.4 87 166 6 5.4 29.5 4.5 1 193 932.0 14.8 39 460 150 3 3.0 30.0 5.0 1 118 981.0 17.2 26 826 167 6 4.9 29.8 4.5 1 211 1,000.0 15.1 50 N