Structural engineers use wireless sensor networks to monitor the condition of dams and bridges. An article describes an experiment in which accelerometers were placed on the Golden Gate Bridge for the purpose of estimating vibration modes. For 18 vertical modes, the system was underdamped (damping ratio < 1). Following are the damping ratios and frequencies for those modes. Damping Ratio Frequency (Hz) Damping Ratio Frequency (Hz)
0.3 2.72 0.5 1.88
0.3 2.84 0.6 0.77
0.3 3.77 0.6 1.26
0.4 2.07 0.6 1.66
0.4 2.2 0.7 0.89
0.4 2.34 0.7 1
0.4 2.61 0.7 0.66
0.5 1.8 0.8 1.13
0.5 1.93 0.8 0.37

Required:
a. Construct a scatterplot of frequency (y)versus damping ratio (x).
b. Compute the least-squares line for predicting frequency from damping ratio.
c. If two modes differ in damping ratio by 0.2, by how much would you predict their frequencies to differ?
d. Predict the frequency for modes with damping ratio 0.75. Round the answer to three decimal places.
e. For what damping ratio would you predict a frequency of 2.0?