11.57 The use of the variable-orifice damper has blossomed in Japan. These dampers provide a mechanically simple and low-power consumer means to protect structures against natural disaster by reducing structural vibrations. Spencer and Nagarajaiah (Journal of Structural Engineering, 2003) give the following data for buildings recently completed or currently under construction.

a Plot the number of semi-active dampers against the height of the tower. Describe the nature of the relation.
b Estimate the relation using the least-squares method.
c Does the number of dampers used increase significantly with the height of the tower? Use .

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Stories Height (m) No. of Semi-active Dampers 11 56.0 42 31 140.5 72 25 119.9 38 28 136.6 60 38 172.0 88 54 241.4 356 19 98.9 27 30 104.9 66 23 100.4 28