The wind chill index represents what the air feels like on exposed skin while factoring in wind

Question:

The wind chill index represents what the air feels like on exposed skin while factoring in wind speed. The wind chill index is determined by considering the wind speed at a height of 5 feet, the typical height of an adult human face. A model for determining wind chill based on the air temperature and wind speed developed by the National Weather Service is

\[W=35.74+0.6215 T-35.75 V+0.4275 T V\]

where \(W\) is the wind chill (in \({ }^{\circ} \mathrm{F}\) )

\(T\) is the air temperature (in \({ }^{\circ} \mathrm{F}\) )

\(V\) is the velocity of the wind (in miles per hour) raised to the 0.16 power (so \(\left.V=v^{0.16}\right)\)

The variable velocity is transformed by raising the actual wind speed to the 0.16 power to account for the nonlinear relation between wind chill and wind speed.

(a) The data in Table 6 show the wind chill temperature for various wind speeds and temperatures. Use the data to draw a scatter diagram of wind chill temperature versus air temperature, treating wind chill temperature as the response variable and using a different plotting symbol for each wind speed. Then draw a scatter diagram of wind chill temperature versus wind speed, treating wind chill temperature as the response variable and using a different plotting symbol for each air temperature.

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(b) Use the model to predict the wind chill temperature if the air temperature is \(3^{\circ} \mathrm{F}\) and the wind speed is 13 miles per hour ( \(\mathrm{mph}\) ).

(c) Interpret the model for a wind speed of \(20 \mathrm{mph}\). Interpret the model for a wind speed of \(30 \mathrm{mph}\).

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