# x18.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; # A0, 1; # 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 = A0 * X0 + A1 * X1 + A2 * X2 + A3 * X3 + A4 * X4. # 7 columns 82 rows Index One Material 1 amount Material 2 amount Material 3 amount Condition Octane number 1 1 55.33 1.72 54 1.66219 92.19 2 1 59.13 1.20 53 1.58399 92.74 3 1 57.39 1.42 55 1.61731 91.88 4 1 56.43 1.78 55 1.66228 92.80 5 1 55.98 1.58 54 1.63195 92.56 6 1 56.16 2.12 56 1.68034 92.61 7 1 54.85 1.17 54 1.58206 92.33 8 1 52.83 1.50 58 1.54998 92.22 9 1 54.52 0.87 57 1.56230 91.56 10 1 54.12 0.88 57 1.57818 92.17 11 1 51.72 0.00 56 1.60401 92.75 12 1 51.29 0.00 58 1.59594 92.89 13 1 53.22 1.31 58 1.54814 92.79 14 1 54.76 1.67 58 1.63134 92.55 15 1 53.34 1.81 59 1.60228 92.42 16 1 54.84 2.87 60 1.54949 92.43 17 1 54.03 1.19 60 1.57841 92.77 18 1 51.44 0.42 59 1.61183 92.60 19 1 53.54 1.39 59 1.51081 92.30 20 1 57.88 1.28 62 1.56443 92.30 21 1 60.93 1.22 62 1.53995 92.48 22 1 59.59 1.13 61 1.56949 91.61 23 1 61.42 1.49 62 1.41330 91.30 24 1 56.60 2.10 62 1.54777 91.37 25 1 59.94 2.29 61 1.65523 91.25 26 1 58.30 3.11 62 1.29994 90.76 27 1 58.25 3.10 63 1.19975 90.90 28 1 55.53 2.88 64 1.20817 90.43 29 1 59.79 1.48 62 1.30621 90.83 30 1 57.51 0.87 60 1.29842 92.18 31 1 62.82 0.88 59 1.40483 91.73 32 1 62.57 0.42 60 1.45056 91.10 33 1 60.23 0.12 59 1.54357 91.74 34 1 65.08 0.10 60 1.68940 91.46 35 1 65.58 0.05 59 1.74695 91.44 36 1 65.64 0.05 60 1.74919 91.56 37 1 65.28 0.42 60 1.78053 91.90 38 1 65.03 0.65 59 1.78104 91.61 39 1 67.84 0.49 54 1.72387 92.09 40 1 73.74 0.00 54 1.73496 90.64 41 1 72.66 0.00 55 1.71966 91.09 42 1 71.31 3.44 55 1.60325 90.51 43 1 72.30 4.02 55 1.66783 90.24 44 1 68.81 6.88 55 1.69836 91.01 45 1 66.61 2.31 52 1.77967 91.90 46 1 63.66 2.99 52 1.81271 91.92 47 1 63.85 0.24 50 1.81485 92.16 48 1 67.25 0.00 53 1.72526 91.36 49 1 67.19 0.00 52 1.86782 92.16 50 1 62.34 0.00 48 2.00677 92.68 51 1 62.98 0.00 47 1.95366 92.88 52 1 69.89 0.00 55 1.89387 92.59 53 1 73.13 0.00 57 1.81651 91.35 54 1 65.09 1.01 57 1.45939 90.29 55 1 64.71 0.61 55 1.38934 90.71 56 1 64.05 1.64 57 1.33945 90.41 57 1 63.97 2.80 60 1.42094 90.43 58 1 70.48 4.64 60 1.57680 89.87 59 1 71.11 3.56 60 1.41229 89.98 60 1 69.05 2.51 60 1.54605 90.00 61 1 71.99 1.28 55 1.55182 89.66 62 1 72.03 1.28 56 1.60390 90.08 63 1 69.90 2.19 56 1.67265 90.67 64 1 72.16 0.51 56 1.55242 90.59 65 1 70.97 0.09 55 1.45728 91.06 66 1 70.55 0.05 52 1.26174 90.69 67 1 69.73 0.06 54 1.28802 91.11 68 1 69.93 0.05 55 1.36399 90.32 69 1 70.60 0.00 55 1.42210 90.36 70 1 75.54 0.00 55 1.67219 90.57 71 1 49.14 0.00 40 2.17140 94.17 72 1 49.10 0.00 42 2.31909 94.39 73 1 44.66 4.99 42 2.14314 93.42 74 1 44.64 3.73 44 2.08081 94.65 75 1 4.23 10.76 41 2.17070 97.61 76 1 5.53 7.99 40 1.99418 97.08 77 1 17.11 5.06 47 1.61437 95.12 78 1 67.60 1.84 55 1.64758 91.86 79 1 64.81 2.24 54 1.69592 91.61 80 1 63.13 1.60 52 1.66118 92.17 81 1 63.48 3.46 52 1.48216 91.56 82 1 62.25 3.56 50 1.49734 92.16