The voltage output (y) of a battery was measured over a
Chapter 8, Problem 8SE(choose chapter or problem)
The voltage output \((y)\) of a battery was measured over a range of temperatures \((x)\) from \(0^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\). The following figure is a scatterplot of voltage versus temperature, with three fitted curves superimposed. The curves are the linear model \(y=\beta_{0}+\beta_{1} x+\varepsilon\), the quadratic model \(y=\beta_{0}+\beta_{1} x+\beta_{2} x^{2}+\varepsilon\), and the cubic model \(y=\beta_{0}+\beta_{1} x+\beta_{2} x^{2}+\beta_{3} x^{3}+\varepsilon\). Based on the plot, which of the models should be used to describe the data? Explain.
i. The linear model.
ii. The quadratic model.
iii. The cubic model.
iv. All three appear to be about equally good.
Equation Transcription:
Text Transcription:
(y)
(x)
0^oC
50^oC
y=beta_0+beta_1x+varepsilon
y=beta_0+1x+beta_2x^2+varepsilon
y=beta_0+1x+beta_2x^2+beta_3x^3+varepsilon
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