Good night my friends:   Nice to see you again, here i go with an exercise that i hope it to be possible to solve. Let get it on!   There has been studied 4 dogs in relation to their growth. This study was related to their weights and its evolution during time. So, I have data from their weights as follows in the table 1:   TABLE 1. RAW OBSERVED DATA DOG AGE_IN_DAYS WEIGHT 1 0 3.5 1 19 4.8 1 47 11.3 1 75 22 1 103 21.5 1 131 34.8 1 159 32.3 1 190 37.1 1 215 42.4 1 243 . 1 272 . 1 299 . 1 327 . 2 0 3.7 2 23 7.7 2 51 14.3 2 79 18 2 107 23.2 2 135 25 2 163 29.3 2 194 33.9 2 219 37.6 2 247 . 2 276 . 2 303 43.2 2 331 43.0 2 359 43.5 2 387 . 2 415 . 3 0 4.9 3 23 6.1 3 50 13.2 3 78 17.2 3 106 20 3 134 25 3 162 28 3 184 29 3 217 32.8 3 246 34.8 3 274 37.4 3 302 36.4 3 330 38.6 3 358 40.4 3 386 37.8 3 414 37.4 3 442 37.2 3 470 35.4 3 498 36.1 3 526 42 3 554 40.4 3 786 64.4 3 814 65.9 4 0 3.5 4 23 7.5 4 50 10.2 4 78 . 4 106 18 4 134 . 4 162 25     Here is the thing, what I need to calculate is the average weight gained between each measure, that means between ages, as follows.   For example, Dog number 2 at age 0, or at birth, showed the weight of 3.7 kg and the next weight was performed at day 23 being 7.7 kg, it means that in 23 days this dog gained 4 kilograms, and it means also that each day the dog gained:   4/23 = 0.17391, it means 173.91 grams gained each day growing. As result of multiplication of this result in grams times 1000, converting this value from kilograms to grams.   With the information in table 1, we need to obtain the 3 last columns as shown in the table 2:   TABLE 2. RAW OBSERVED DATA, PLUS LAST 2 COLUMNS WITH KILOGRAMS AND GRAMS GAINED BY DAY DOG AGE_IN_DAYS WEIGHT days_between_measure kg_gained gr_gained_by_day 1 0 3.5 . . . 1 19 4.8 19 1.30 68.42 1 47 11.3 28 6.50 232.14 1 75 22 28 10.7 382.14 1 103 21.5 28 -0.5 -17.86 1 131 34.8 28 13.30 475.00 1 159 32.3 28 -2.50 -89.29 1 190 37.1 31 4.80 154.84 1 215 42.4 25 5.30 212.00 2 0 3.7 . . . 2 23 7.7 23 4.00 173.91 2 51 14.3 28 6.60 235.71 2 79 18 28 3.70 132.14 2 107 23.2 28 5.20 185.71 2 135 25 28 1.80 64.29 2 163 29.3 28 4.30 153.57 2 194 33.9 31 4.60 148.39 2 219 37.6 25 3.70 148.00 2 247 . . . . 2 276 . . . . 2 303 43.2 84 5.60 66.67 2 331 43 28 -0.20 -7.14 2 359 43.5 28 0.50 17.86 2 387 . . . . 2 415 . . . . 3 0 4.9 . . . 3 23 6.1 23 1.20 52.17 3 50 13.2 27 7.10 262.96 3 78 17.2 28 4.00 142.86 3 106 20 28 2.80 100.00 3 134 25 28 5.00 178.57 3 162 28 28 3.00 107.14 3 184 29 22 1.00 45.45 3 217 32.8 33 3.80 115.15 3 246 34.8 29 2.00 68.97 3 274 37.4 28 2.60 92.86 3 302 36.4 28 -1.00 -35.71 3 330 38.6 28 2.20 78.57 3 358 40.4 28 1.80 64.29 3 386 37.8 28 -2.60 -92.86 3 414 37.4 28 -0.40 -14.29 3 442 37.2 28 -0.20 -7.14 3 470 35.4 28 -1.80 -64.29 3 498 36.1 28 0.70 25.00 3 526 42 28 5.90 210.71 3 554 40.4 28 -1.60 -57.14 3 786 64.4 232 24.00 103.45 3 814 65.9 28 1.50 53.57 4 0 3.5 . . . 4 23 7.5 23 4.00 173.91 4 50 10.2 27 2.70 100.00 4 78 . .     4 106 18 56 7.80 139.29 4 134 . .     4 162 25 56 7.00 125.00   From here, what have to be obtained is the corrected weight each 20 days of live for each dog, i'll try to explain this in the next paragraphs.   If you look carefully each measure, at its corresponding line, has its own kilogram gained and grams gained by day. This value could be negative, it does not matter cause dogs often loose weight, this is pretty normal. Therefore, the question is I need to obtain the adjusted weight each 20 days from birth to further ages: 20, 40, 60, 80 and so on until the dog dies and has no more measures. This happens when the next information is at age 0 corresponding to the next dog.   For a better representation I will use dog 3 and its measures at day 50 and 78.   Dog 3 at 50 days old weighted 13.2 Kg, then at 78 days old he weighted 17.2. It means that in 28 days this do gained 4 kilograms, one more time as follows:   4/28 = 0.14285, it means 142.85 grams gained each day growing from 50 to 78 days old.   The question is: If I have these, and their corresponding daily gains weights, I can estimate other measures in other ages, for example each 20 days. I wanted to point out these measures because if I want to estimate the weight at 60 days old of the dog I can use this information of the 50 and 78 days old, having the estimate gain in grams each day I can estimate the weight at 60 days like this:     [(weight gain in grams between 2 measures)*(age to estimate weight-first age measured)] + weight at first age measured   [(142.85 grams)*(60-50)]+weight at 50 days = [(142.85)*10]+13.2 = 1.4285+13.2 = 14.6285 kg at 60 days.   From now, and using the table above obtained, we need to obtain the corrected weight at corresponding each 20 days, as follows in the next table:   DOG AGE_IN_DAYS WEIGHT days_between_measure kg_gained gr_gained_by_day new_age weight_at_new_age 1 0 3.5 . . . .   1 19 4.8 19 1.30 68.42 20 5.03214 1 47 11.3 28 6.50 232.14 40 9.67500 1 75 22 28 10.70 382.14 60 16.26786 1 103 21.5 28 -0.50 -17.86 80 21.91071 1 131 34.8 28 13.30 475.00 100 21.55357 1 159 32.3 28 -2.50 -89.29 120 29.57500 1 190 37.1 31 4.80 154.84 140 33.99643 1 215 42.4 25 5.30 212.00 160 32.45484 1 243 . 28 . . 180 35.55161 1 272 . 29 . . 200 39.22000 1 299 . 27 . . 220 . 1 327 . 28 . . 240 . 2 0 3.7 . . . 20 7.17826 2 23 7.7 23 4.00 173.91 40 11.70714 2 51 14.3 28 6.60 235.71 60 15.48929 2 79 18 28 3.70 132.14 80 18.18571 2 107 23.2 28 5.20 185.71 100 21.90000 2 135 25 28 1.80 64.29 120 24.03571 2 163 29.3 28 4.30 153.57 140 25.76786 2 194 33.9 31 4.60 148.39 160 33.00968 2 219 37.6 25 3.70 148.00 180 36.41600 2 247 . 28 . . 200 34.78800 2 276 . 29 . . 220 37.74800 2 303 43.2 27 . . 240 40.70800 2 331 43 28 -0.20 -7.14 260 43.66800 2 359 43.5 28 0.50 17.86 280 46.62800 2 387 . 28 . . 300 49.58800 2 415 . 28 . . 320 43.07857 2 . . . . . 340 43.16071 3 0 4.9 . . . 20 5.94348 3 23 6.1 23 1.20 52.17 40 10.57037 3 50 13.2 27 7.10 262.96 60 14.62857 3 78 17.2 28 4.00 142.86 80 17.40000 3 106 20 28 2.80 100.00 100 19.40000 3 134 25 28 5.00 178.57 120 22.50000 3 162 28 28 3.00 107.14 140 25.64286 3 184 29 22 1.00 45.45 160 27.78571 3 217 32.8 33 3.80 115.15 180 28.81818 3 246 34.8 29 2.00 68.97 200 30.84242 3 274 37.4 28 2.60 92.86 220 33.00690 3 302 36.4 28 -1.00 -35.71 240 34.38621 3 330 38.6 28 2.20 78.57 260 36.10000 3 358 40.4 28 1.80 64.29 280 37.18571 3 386 37.8 28 -2.60 -92.86 300 36.47143 3 414 37.4 28 -0.40 -14.29 320 37.81429 3 442 37.2 28 -0.20 -7.14 340 39.24286 3 470 35.4 28 -1.80 -64.29 360 40.21429 3 498 36.1 28 0.70 25.00 380 38.35714 3 526 42 28 5.90 210.71 400 37.60000 3 554 40.4 28 -1.60 -57.14 420 37.35714 3 786 64.4 232 24.00 103.45 440 37.21429 3 814 65.9 28 1.50 53.57 460 37.32857 3 . . . . . 480 35.65000 3 . . . . . 500 36.52143 3 . . . . . 520 40.73571 3 . . . . . 540 41.20000 3 . . . . . 560 41.02069 3 . . . . . 780 63.77931 3 . . . . . 800 65.15000 4 0 3.5 . . . 20 6.97826 4 23 7.5 23 4.00 173.91 40 9.20000 4 50 10.2 27 2.70 100.00 60 11.59286 4 78 . .     80 14.37857 4 106 18 56 7.80 139.29 100 17.16429 4 134 . .     120 19.75000 4 162 25 56 7.00 125.00 140 22.25000   With the prerogative, IT IS NEEDED TO ESTIMATE THE WEIGHT OF EACH DOG EACH 20 DAYS.    Each example i post here, i try to make it very useful to be helped easily, so the colors in the table 3, what is thought to be achieved, are going to help in the estimations, because those are special cases because the data of each dog is special. Here we go:   As said repetitively, each 20 days must appear the new weight for each dog. As seen in Table 3, dog 1 has its first recorded weight at 19 days old, it means that this weight can not be used to estimate the weight at 20 days old of this dog, meanwhile for dog 2 and 3 they have their respective first weight at day 23, for that reason it can be estimated the weight at day 20, and this measure is allocated at the same line that the weight at age 0, indicating that dogs with its second weight less than 20 days old will be its first estimated weight at 20 days in the second line, and those with the second weight with more than 20 days can have the new estimated weight at 20 days in the same line that the weight at age 0.   Else, for dog 1 (for weigh at 19 and 47) and for dog 3 (for weigh at 78 and 47) it can be observed that the new estimated measures at days 20 and 40 for dog 1, and at days 80 and 100 for dog 3, are used to estimate two new weights, using just 2 measures.   Next, in green color it can be observed that the new estimated measures are not located in the same line that the weights used to their respective estimation. It can be noted that these two estimations are result of their respective upper and lower ages. Describing this with details:   In dog 1 for estimated weights at 80 and 100 days of age, its used the recorded weight at 75 and 103 days, and those new estimates are located not in the same line that the corresponding line, those values are located in new rows below the last new estimated values, for this i will take this to see it here:   DOG AGE_IN_DAYS WEIGHT days_between_measure kg_gained gr_gained_by_day new_age weight_at_new_age 1 75 22 28 10.70 382.14 60 16.26786 1 103 21.5 28 -0.50 -17.86 80 21.91071 1 131 34.8 28 13.30 475.00 100 21.55357   This can be observed also for the dog 2, for the estimated values for 140 and 160 ages, as seen in the TABLE 3:   DOG AGE_IN_DAYS WEIGHT days_between_measure kg_gained gr_gained_by_day new_age weight_at_new_age 2 135 25 28 1.80 64.29 120 24.03571 2 163 29.3 28 4.30 153.57 140 25.76786 2 194 33.9 31 4.60 148.39 160 33.00968   Related case can be observed for dog 3 and for estimation of the new weight at 220 and 240 ages because the new data are in rows after the original data used to their estimation:   DOG AGE_IN_DAYS WEIGHT days_between_measure kg_gained gr_gained_by_day new_age weight_at_new_age 3 217 32.8 33 3.80 115.15 180 28.81818 3 246 34.8 29 2.00 68.97 200 30.84242 3 274 37.4 28 2.60 92.86 220 33.00690 3 302 36.4 28 -1.00 -35.71 240 34.38621   Special cases can be observed in Dog 2 and in Dog 4, where no weights measures were taken for 247 and 276 days for the first one and the day 78 and 134, for the dog 4. In both cases the used values to estimate the middle values were the weights at 219 and 303 days in dog 2 and weight at ages 50, 106 and 134 for dog 4.   In dog 2, can be observed that the difference between days 219 and 303 is 84 dais, in these period the dog gained 5.6 kilograms and 66,67 grams per day, and using this information were estimated weights at 220, 240, 260 280 and 300 days of age, as shown in Table 3:   DOG AGE_IN_DAYS WEIGHT days_between_measure kg_gained gr_gained_by_day new_age weight_at_new_age 2 219 37.6 25 3.70 148.00 180 36.41600 2 247 . 28 . . 200 34.78800 2 276 . 29 . . 220 37.74800 2 303 43.2 27 . . 240 40.70800 2 331 43 28 -0.20 -7.14 260 43.66800 2 359 43.5 28 0.50 17.86 280 46.62800 2 387 . 28 . . 300 49.58800   The other special case is shown in dog 4 where the is many missing data, where   In this case, the dog was not measured in relation to it weight at 78 and 134 days of age, but the other measures are recorded. In this case to estimate weights for 60, 80 and 100 days were used the recorded weights at 50 and 106 days, witch difference was 56 days with an gained weight of 7.8 kilograms and 139.29 grams per day. In the same context, to estimate weight for 120, 140 and 160 days of age were user the weights at 106 and 162 years of age. DOG AGE_IN_DAYS WEIGHT days_between_measure kg_gained gr_gained_by_day new_age weight_at_new_age 4 0 3.5 . . . 20 6.97826 4 23 7.5 23 4.00 173.91 40 9.20000 4 50 10.2 27 2.70 100.00 60 11.59286 4 78 . .     80 14.37857 4 106 18 56 7.80 139.29 100 17.16429 4 134 . .     120 19.75000 4 162 25 56 7.00 125.00 140 22.25000     Finally, it can be pointed out that the observations for each dog ends where the value for age of the next dog is equal to zero, so i guess the loop to be applied for each animal. With this, the table to be obtained, again, is:   DOG AGE_IN_DAYS WEIGHT days_between_measure kg_gained gr_gained_by_day new_age weight_at_new_age 1 0 3.5 . . . .   1 19 4.8 19 1.30 68.42 20 5.03214 1 47 11.3 28 6.50 232.14 40 9.67500 1 75 22 28 10.70 382.14 60 16.26786 1 103 21.5 28 -0.50 -17.86 80 21.91071 1 131 34.8 28 13.30 475.00 100 21.55357 1 159 32.3 28 -2.50 -89.29 120 29.57500 1 190 37.1 31 4.80 154.84 140 33.99643 1 215 42.4 25 5.30 212.00 160 32.45484 1 243 . 28 . . 180 35.55161 1 272 . 29 . . 200 39.22000 1 299 . 27 . . 220 . 1 327 . 28 . . 240 . 2 0 3.7 . . . 20 7.17826 2 23 7.7 23 4.00 173.91 40 11.70714 2 51 14.3 28 6.60 235.71 60 15.48929 2 79 18 28 3.70 132.14 80 18.18571 2 107 23.2 28 5.20 185.71 100 21.90000 2 135 25 28 1.80 64.29 120 24.03571 2 163 29.3 28 4.30 153.57 140 25.76786 2 194 33.9 31 4.60 148.39 160 33.00968 2 219 37.6 25 3.70 148.00 180 36.41600 2 247 . 28 . . 200 34.78800 2 276 . 29 . . 220 37.74800 2 303 43.2 27 . . 240 40.70800 2 331 43 28 -0.20 -7.14 260 43.66800 2 359 43.5 28 0.50 17.86 280 46.62800 2 387 . 28 . . 300 49.58800 2 415 . 28 . . 320 43.07857 2 . . . . . 340 43.16071 3 0 4.9 . . . 20 5.94348 3 23 6.1 23 1.20 52.17 40 10.57037 3 50 13.2 27 7.10 262.96 60 14.62857 3 78 17.2 28 4.00 142.86 80 17.40000 3 106 20 28 2.80 100.00 100 19.40000 3 134 25 28 5.00 178.57 120 22.50000 3 162 28 28 3.00 107.14 140 25.64286 3 184 29 22 1.00 45.45 160 27.78571 3 217 32.8 33 3.80 115.15 180 28.81818 3 246 34.8 29 2.00 68.97 200 30.84242 3 274 37.4 28 2.60 92.86 220 33.00690 3 302 36.4 28 -1.00 -35.71 240 34.38621 3 330 38.6 28 2.20 78.57 260 36.10000 3 358 40.4 28 1.80 64.29 280 37.18571 3 386 37.8 28 -2.60 -92.86 300 36.47143 3 414 37.4 28 -0.40 -14.29 320 37.81429 3 442 37.2 28 -0.20 -7.14 340 39.24286 3 470 35.4 28 -1.80 -64.29 360 40.21429 3 498 36.1 28 0.70 25.00 380 38.35714 3 526 42 28 5.90 210.71 400 37.60000 3 554 40.4 28 -1.60 -57.14 420 37.35714 3 786 64.4 232 24.00 103.45 440 37.21429 3 814 65.9 28 1.50 53.57 460 37.32857 3 . . . . . 480 35.65000 3 . . . . . 500 36.52143 3 . . . . . 520 40.73571 3 . . . . . 540 41.20000 3 . . . . . 560 41.02069 3 . . . . . 780 63.77931 3 . . . . . 800 65.15000 4 0 3.5 . . . 20 6.97826 4 23 7.5 23 4.00 173.91 40 9.20000 4 50 10.2 27 2.70 100.00 60 11.59286 4 78 . . . . 80 14.37857 4 106 18 56 7.80 139.29 100 17.16429 4 134 . . . . 120 19.75000 4 162 25 56 7.00 125.00 140 22.25000   After this, and transposing this table, the new data would be:   DOG 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 700 720 740 760 780 800 1 3.5000 5.0321 9.6750 16.2679 21.9107 21.5536 29.5750 33.9964 32.4548 35.5516 39.2200 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.7000 7.1783 11.7071 15.4893 18.1857 21.9000 24.0357 25.7679 33.0097 36.4160 34.7880 37.7480 40.7080 43.6680 46.6280 49.5880 43.0786 43.1607 . . . . . . . . . . . . . . . . . . . . . . . 3 4.9000 5.9435 10.5704 14.6286 17.4000 19.4000 22.5000 25.6429 27.7857 28.8182 30.8424 33.0069 34.3862 36.1000 37.1857 36.4714 37.8143 39.2429 40.2143 38.3571 37.6000 37.3571 37.2143 37.3286 35.6500 36.5214 40.7357 41.2000 41.0207 . . . . . . . . . . 63.7793 65.1500 4 3.5000 6.9783 9.2000 11.5929 14.3786 17.1643 19.7500 22.2500 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   where in the first column appears the dogs evaluated, and in the next columns are the new estimated weights each 20 days.   I hope to be helped.   Thank you very much                        ... 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Good day SAS friends: I have this data set:   data have; input SIRE DAM WEIGHT IA_NUMBER; WEIGHTxIA_NUMBER = WEIGHT*IA_NUMBER; cards; 1 1 35 2 1 2 47 1 1 3 60 1 1 4 51 1 1 5 65 2 1 6 77 3 2 7 40 1 2 8 51 5 2 9 54 4 2 10 63 2 2 11 70 6 3 12 37 1 3 13 37 1 3 14 49 1 3 15 53 5 ; proc GLM data = have; class SIRE DAM; model WEIGHT IA_NUMBER = SIRE; run;   This data set can be find in this book:   http://www.livrosabertos.sibi.usp.br/portaldelivrosUSP/catalog/view/162/147/713-1   The first two ANOVAS are easy to find, the problem is when the autor call the products of WEIGHT and IA_NUMBER, wich Analisys of CO-variance between  WEIGHT and IA_NUMBER  would be:     Variance Font Freedom degrees Product Sumatory Medium Product Sire 2 25.5 12.75 Residual 12 114.9 9.58 Total 14 140.4       This result appears in page 194 of the same book.   Thanks in advance for the tip.   Regards ... View more