Structural engineers use wireless sensor networks to monitor the condition of dams and bridges. An experiment was conducted in which accelerometers were placed on the Golden Gate Bridge for the purpose of estimating vibration modes. The study measured damping ratios and frequencies (in Hz) for vertical modes. The data are as follows:
Damping Ratio Frequency(Hz) Damping Ratio Frequency (Hz)
0.3 2.72 0.3 2.84
0.3 3.77 0.4 2.07
0.4 2.20 0.4 2.34
0.4 2.61 0.5 1.80
0.5 1.93 0.5 1.53
0.6 0.77 0.6 1.26
0.7 1.66 0.7 0.89
0.7 1.00 0.8 0.66
a. Construct a scatterplot of frequency (y)versus damping ratio (x). Verify that a linear model is appropriate.
b. Compute the least-squares line for predicting frequency from damping ratio. Round the answers to three decimal places.