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Unformatted text preview: will occur at the vertex of the parabola. Recalling the
Vertex Formula, Equation 2.4, x = − 2ba ≈ − 2(−.0.321) ≈ 14.741. This corresponds to roughly 2 : 45
PM. To ﬁnd the temperature, we substitute x = 14.741 into y = −0.321x2 + 9.464x − 45.857 to get
y ≈ 23.899, or 23.899◦ F.
The results of the last example should remind you that regression models are just that, models. Our
predicted warmest temperature was found to be 23.899◦ F, but our data says it will warm to 24◦ F.
It’s all well and good to observe trends and guess at a model, but a more thorough investigation
into why certain data should be linear or quadratic in nature is usually in order - and that, most
often, is the business of scientists. 2.5 Regression 2.5.1 175 Exercises 1. Using the energy production data given below
(in Quads) 1950 1960 1970 1980 1990 2000 35.6 42.8 63.5 67.2 70.7 71.2 (a) Plot the data using a graphing calculator and explain why it does not appear to be
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