Chapter 7, Problem 12SE

A materials scientist is experimenting with a new material with which to make beverage cans. She fills cans with liquid at room temperature, and then refrigerates them to see how fast they cool. According to Newton’s law of cooling, if t is the time refrigerated and y is the temperature drop at time t, then y is related to t by an equation of the form

$\ln y={\beta }_0+{\beta }_{1}t$,

where β₀ is a constant that depends on the initial temperature of the can and the ambient temperature of the refrigerator, and β₁ is a constant that depends on the physical properties of the can. The scientist measures the temperature at regular intervals, and then fits this model to the data. The results are shown in the following figure. A scatterplot, with the least-squares line superimposed, is on the left, and the residual plot is on the right.

What should the scientist do next?

1. i. Try to find a transformation that makes the relationship more linear.
2. ii. Use the model as is, because Newton’s law of cooling is a physical law.
3. iii. Use the model as is, because it fits well enough.
4. iv. Carefully examine the experimental setup to sec what might have gone wrong.