3. Data were collected from three anemometers in the 3x3 wind tunnel behind Guggenheim Hall. The three anemometers are a Davis anemometer, a sonic anemometer, and a NIST-calibrated anemometer (Young anemometer). The Young anemometer gives a voltage Vyoung proportional to wind speed, and the NIST-certified calibration equation is UNIST = C V Young + d, where c = 12.12 0.08 m s V, d = 0.08 0.05 m s, and UNIST is the NIST wind speed in m s. The table below shows the mean "wind speed" (in this case, voltage in V or rotation rates in # rotations per 200 seconds) for each anemometer for four different wind speeds that were measured, including the standard deviation of the mean for each: Wind speed VYoung (V) Vyoung (V) RDavis (r/200 s) RDavis Vsonic OV Sonic (r/200 s) (V) (V) 1234 0.758 0.0168 3.115 0.846 0.452 0.003840 1.273 0.0250 2.713 0.954 0.749 0.006252 1.719 2.093 0.0329 3.66 0.475 1.002 0.009226 0.0417 4.45 0.499 1.222 0.008688 a. You have an equation relating UNIST and VYoung above. There are also linear relationships among the other anemometers: Vyoung = eRDavis + f and V Young = gVsonic + h that you do not know all the details of but now have the tools to calculate. Perform linear regressions to calculate the values of the slopes (e, g) and intercepts (f, h) as well as their errors. (Hint: recall the code used in question 4 of Homework 1!) [20 points] b. Using the equations derived in the previous part, come up with two equations: one relating UNIST and RDavis and one relating UNIST and Vsonic. These equations will convert the units of V and r/200 s into wind speeds that can be directly compared! [15 points] c. Populate the missing values in the table below using your equations relating UNIST to each of the three anemometers. All of your values should be in m s. [20 points] Wind Speed 1 2 34 Young U [ms] Davis Sonic