# x17.txt # # Reference: # # Helmut Spaeth, # Mathematical Algorithms for Linear Regression, # Academic Press, 1991, # ISBN 0-12-656460-4. # # F S Wood, # The Use of Individual Effects and Residuals in Fitting Equations to Data, # Technometrics, Volume 15, 1973, pages 677-695. # # Discussion: # # In the investigation of the manufacturing process in a refinery, # the octane rating of a particular petrol was measured as a # function of the 3 raw materials, # and a variable that characterized the manufacturing conditions. # # There are 82 rows of data. The data include: # # I, the index; # A1, amount of material 1; # A2, amount of material 2; # A3, amount of material 3; # A4, manufacturing condition rating; # B, the octane rating; # # We seek a model of the form: # # B = A1 * X1 + A2 * X2 + A3 * X3 + A4 * X4. # 6 columns 82 rows Index Material 1 amount Material 2 amount Material 3 amount Condition Octane number 1 55.33 1.72 54 1.66219 92.19 2 59.13 1.20 53 1.58399 92.74 3 57.39 1.42 55 1.61731 91.88 4 56.43 1.78 55 1.66228 92.80 5 55.98 1.58 54 1.63195 92.56 6 56.16 2.12 56 1.68034 92.61 7 54.85 1.17 54 1.58206 92.33 8 52.83 1.50 58 1.54998 92.22 9 54.52 0.87 57 1.56230 91.56 10 54.12 0.88 57 1.57818 92.17 11 51.72 0.00 56 1.60401 92.75 12 51.29 0.00 58 1.59594 92.89 13 53.22 1.31 58 1.54814 92.79 14 54.76 1.67 58 1.63134 92.55 15 53.34 1.81 59 1.60228 92.42 16 54.84 2.87 60 1.54949 92.43 17 54.03 1.19 60 1.57841 92.77 18 51.44 0.42 59 1.61183 92.60 19 53.54 1.39 59 1.51081 92.30 20 57.88 1.28 62 1.56443 92.30 21 60.93 1.22 62 1.53995 92.48 22 59.59 1.13 61 1.56949 91.61 23 61.42 1.49 62 1.41330 91.30 24 56.60 2.10 62 1.54777 91.37 25 59.94 2.29 61 1.65523 91.25 26 58.30 3.11 62 1.29994 90.76 27 58.25 3.10 63 1.19975 90.90 28 55.53 2.88 64 1.20817 90.43 29 59.79 1.48 62 1.30621 90.83 30 57.51 0.87 60 1.29842 92.18 31 62.82 0.88 59 1.40483 91.73 32 62.57 0.42 60 1.45056 91.10 33 60.23 0.12 59 1.54357 91.74 34 65.08 0.10 60 1.68940 91.46 35 65.58 0.05 59 1.74695 91.44 36 65.64 0.05 60 1.74919 91.56 37 65.28 0.42 60 1.78053 91.90 38 65.03 0.65 59 1.78104 91.61 39 67.84 0.49 54 1.72387 92.09 40 73.74 0.00 54 1.73496 90.64 41 72.66 0.00 55 1.71966 91.09 42 71.31 3.44 55 1.60325 90.51 43 72.30 4.02 55 1.66783 90.24 44 68.81 6.88 55 1.69836 91.01 45 66.61 2.31 52 1.77967 91.90 46 63.66 2.99 52 1.81271 91.92 47 63.85 0.24 50 1.81485 92.16 48 67.25 0.00 53 1.72526 91.36 49 67.19 0.00 52 1.86782 92.16 50 62.34 0.00 48 2.00677 92.68 51 62.98 0.00 47 1.95366 92.88 52 69.89 0.00 55 1.89387 92.59 53 73.13 0.00 57 1.81651 91.35 54 65.09 1.01 57 1.45939 90.29 55 64.71 0.61 55 1.38934 90.71 56 64.05 1.64 57 1.33945 90.41 57 63.97 2.80 60 1.42094 90.43 58 70.48 4.64 60 1.57680 89.87 59 71.11 3.56 60 1.41229 89.98 60 69.05 2.51 60 1.54605 90.00 61 71.99 1.28 55 1.55182 89.66 62 72.03 1.28 56 1.60390 90.08 63 69.90 2.19 56 1.67265 90.67 64 72.16 0.51 56 1.55242 90.59 65 70.97 0.09 55 1.45728 91.06 66 70.55 0.05 52 1.26174 90.69 67 69.73 0.06 54 1.28802 91.11 68 69.93 0.05 55 1.36399 90.32 69 70.60 0.00 55 1.42210 90.36 70 75.54 0.00 55 1.67219 90.57 71 49.14 0.00 40 2.17140 94.17 72 49.10 0.00 42 2.31909 94.39 73 44.66 4.99 42 2.14314 93.42 74 44.64 3.73 44 2.08081 94.65 75 4.23 10.76 41 2.17070 97.61 76 5.53 7.99 40 1.99418 97.08 77 17.11 5.06 47 1.61437 95.12 78 67.60 1.84 55 1.64758 91.86 79 64.81 2.24 54 1.69592 91.61 80 63.13 1.60 52 1.66118 92.17 81 63.48 3.46 52 1.48216 91.56 82 62.25 3.56 50 1.49734 92.16