Wind Chill Problem: When the wind is blowing on a cold day, the temperature seems to be

Chapter 8, Problem 6

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Wind Chill Problem: When the wind is blowing on a cold day, the temperature seems to be colder than it really is. For any given actual temperature with no wind, the equivalent temperature due to wind chill is a function of wind speed. Figure 8-4k and the table show data published by NOAA (the National Oceanographic and Atmospheric Administration) (see www.ncdc.gov/ol/climate/ conversion/windchillchart.html). a. Ignoring the data point at 0 mi/hr, run a logarithmic regression to find the bestfitting logarithmic function. Plot it and the data on the same screen. Sketch the result. b. At what wind speed does the logarithmic function predict that the equivalent temperature would be 0F? Do you find this number by extrapolation or by interpolation? Explain why an untranslated exponential function would predict that the equivalent temperature would never be zero. Explain why the logarithmic function does not have the correct endpoint behavior at the left end of the domain. c. Make a residual plot for the logarithmic function. Sketch the result. Do the residuals follow a pattern? What does this fact tell you about how well the logarithmic function fits the data? d. Check the NOAA Web site mentioned previously to find out the mathematical model NOAA actually uses to compute wind-chill-equivalent temperatures.