The Following Time-Of-Day and Temperature (F ^$\circ$ ) Were Gathered During a Gorgeous Midsummer Day in Fargo

question 42

Essay

The following time-of-day and temperature (F ^$\circ$ ) were gathered during a gorgeous midsummer day in Fargo, North Dakota:
$$\begin{array} { | c | c | } \hline \text { Time of Day } & \text { Temperature } \\\hline 18 & 74 \\\hline 17 & 73 \\\hline 16 & 73 \\\hline 15 & 72 \\\hline 14 & 70 \\\hline 13 & 70 \\\hline 12 & 68 \\\hline 11 & 66 \\\hline 10 & 63 \\\hline 9 & 62 \\\hline 8 & 59 \\\hline 7 & 58 \\\hline\end{array}$$
Source: National Weather Service; www.weather.gov
(a) Make a scatter plot of these data.
(b) Fit a linear model to the data.
(c) Fit an exponential model to the data.
(d) Fit a quadratic model to the data.(e) Use your equations to make a table showing the predicted temperature for each model, rounded to the nearest degree.
(f) The actual temperature at 8:00 p.m. (20 hours) was 70° F. Which model was closest? Which model was second-closest?
(g) All of the models give values that are too high for each of the times after 6:00 PM. What is one possible explanation for this?

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