The voltage output (y) of a battery was measured over a range of temperatures (x) from 0°C to 50°C. The following figure is a scatterplot of voltage versus temperature, with three fitted curves superimposed. The curves are the linear model y = β₀+ β₁x + ε, the quadratic model y = β₀+ β₁x = β₂x²+ ε, and the cubic model y = β₀+ β₁x + β₂x²+ β₃x³+ ε. 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.

Transcribed Image Text:

115 110 105 100 95 90 85 10 20 30 40 50 Temperature (°C) Voltage output (V)