According to the National Weather Service, the average monthly high temperature in the Dallas/Fort Worth, Texas area from the years of 2006-2008 is given by the following table:MonthAverage Maximum Monthly TemperatureJan48.1Feb50.9Mar62.4Apr67.0May76.5Jun83.9Jul86.8Aug88.1Sep79.2Oct69.9Nov59.5Dec49.6Plot the data on a scatter plot. Produce a sine regression model for the data. Round the values for a, b, c, and d to the nearest 0.001. Using the sine regression model predict what the temperature would be given y(30). Analyze your prediction and explain why your prediction may or may not be accurate. If it might not be accurate, explain what might make the information more accurate.
Answer
A
Accurate, nothing would help it be more accurate.
B
May not be accurate, weather is changing all the time; Information from various states would help make the information more accurate.
C
Accurate, it is easily predictable.
D
May not be accurate, information was taken over 2 year period; More information from previous years would help the prediction be more accurate.
Explanation
The data give average temperatures for each month based on only the years 2006–2008. A sine model captures the seasonal pattern, but its prediction at y(30) is still an estimate and may not reflect unusual weather or longer-term climate variation. Using temperature records from more previous years would provide a stronger basis for estimating the pattern. Therefore, the best choice is “May not be accurate, information was taken over 2 year period; More information from previous years would help the prediction be more accurate.”
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