The article Seismic Hazard in Greece Based on Different Strong Ground Motion Parameters (S. Koutrakis, G. Karakaisis,

The article €œSeismic Hazard in Greece Based on Different Strong Ground Motion Parameters€ (S. Koutrakis, G. Karakaisis, et al., Journal of Earthquake Engineering, 2002:75€“109) presents a study of seismic events in Greece during the period 1978€“1997. Of interest is the duration of €œstrong ground motion,€ which is the length of time that the acceleration of the ground exceeds a specified value. For each event, measurements of the duration of strong ground motion were made at one or more locations. Table SE22 presents, for each of 121 such measurements, the data for the duration of time y (in seconds) that the ground acceleration exceeded twice the acceleration due to gravity, the magnitude m of the earthquake, the distance d (in km) of the measurement from the epicenter, and two indicators of the soil type s₁and s₂, defined as follows: s₁= 1 if the soil consists of soft alluvial deposits, s₁= 0 otherwise, and s₂= 1 if the soil consists of tertiary or older rock, s₂= 0 otherwise. Cases where both s₁= 0 and s₂= 0 correspond to intermediate soil conditions. The article presents repeated measurements at some locations, which we have not included here.

TABLE SE22 Data for Exercise 22

Use the data in Table SE22 to construct a linear model to predict duration y from some or all of the variables m, d, s₁, and s₂. Be sure to consider transformations of the variables, as well as powers of and interactions between the independent variables. Describe the steps taken to construct your model. Plot the residuals versus the fitted values to verify that your model satisfies the necessary assumptions. In addition, note that the data are presented in chronological order, reading down the columns. Make a plot to determine whether time should be included as an independent variable.

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y d S1 S2 y m d S1 S2 y m d S1 S2 8.82 6.4 30 1 4.31 5.3 5.74 5.6 15 4.08 5.2 7 28.27 6.6 31 1 5.13 6.9 128 1 15.90 6.9 105 1 17.94 6.9 33 3.20 5.1 13 6.04 5.8 15 3.60 5.4 7.29 5.2 19 1 0.15 4.9 16 1 7.98 5.3 12 1 0.02 7.03 2.17 6.2 68 1 5.06 6.2 75 1 16.23 6.2 13 5.4 10 0.01 6.6 119 1 3.67 6.6 85 1 5.1 45 1 4.13 5.1 10 1 6.44 5.2 5.3 21 4.27 5.2 18 1 22 12 17 0.02 5.3 1 10.45 11 1 2.25 4.8 14 1 2.14 4.5 5.2 1 8.32 5.43 5.5 5.2 22 49 1 3.10 6.18 5.5 5.2 15 13 4.41 1 17.19 5.9 9 4.78 5.5 1 4.56 5.5 1 5.14 5.5 10 1 2.82 5.5 20 1 0.94 5.0 6 1 0.05 4.9 14 1 3.51 5.7 22 2.85 4.6 21 1 20.00 5.8 16 1 13.92 5.8 34 1 4.21 4.7 20 1 12.04 6.1 31 3.96 6.1 44 1.93 5.7 39 1 0.87 5.0 65 1 6.91 5.4 16 1.56 5.0 44 1 0.62 4.8 11 1 5.63 5.3 1 5.03 5.1 2 1 8.10 5.4 12 1 0.10 5.2 21 1 0.51 4.9 14 1 1.30 5.8 34 1 5.10 4.8 16 1 13.14 5.6 5 1 11.92 5.6 5 16.52 5.5 15 1 8.16 5.5 12 1 3.93 5.7 65 1 19.84 5.7 50 1 10.04 5.1 28 1 2.00 5.4 27 1 1.65 5.4 27 1 0.79 5.4 35 0.43 5.4 31 1 1.75 5.4 30 1 0.02 5.4 32 1 14.22 6.5 20 1 6.37 6.5 90 1 0.10 6.5 61 1 0.06 6.5 72 1 2.78 2.14 4.9 8 5.43 5.2 9 1.48 5.2 27 5.2 22 0.81 4.6 3.27 5.1 12 0.92 5.2 4.8 29 0.73 5.2 22 6.36 5.2 14 3.18 15 11.18 5.0 0.18 5.0 19 1.20 5.0 19 2.54 4.5 6. 0.31 4.5 12 4.37 4.7 5 1.55 4.7 13 1 4.7 1.90 0.29 6.26 12 1.02 5.0 14 0.01 4.5 17 4.7 6.3 5 1 1 0.71 4.8 6.3 4 9 1 0.21 0.04 0.01 4.8 4.5 5 3 1 9. 4.27 1 1 3.44 5.4 4 1 3.25 5.4 4 1 4.5 1 1 2.32 5.4 5 1 0.90 4.7 4 1 1.19 4.7 3 1 1.49 5.0 4 1 0.37 5.0 4 1 2.66 5.4 1 1 2.85 0.01 9.34 5.4 1 1 21.07 6.4 78 1 7.47 6.4 104 0.04 15.30 6.4 86 1 6.4 105 1 30.45 6.6 51 1 6.6 116 1 6.6 82 1 12.78 6.6 65 1 10.47 6.6 117 0 00-