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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Definitions:

Actual Output

The actual total value of goods and services produced by an economy over a specific period.

Potential Output

Potential output refers to the maximum amount of goods and services an economy can produce when it uses its resources fully and efficiently, without prompting inflation.

Cash Conversion Cycle

A metric that expresses the duration (in days) it takes for a company to convert its investments in inventory and other resources into cash flows from sales.

DSO

Days Sales Outstanding, a measure of the average number of days that a company takes to collect revenue after a sale has been made.