Question

1. which of the following represents a situation that would most likely be modeled by linear regression? a) the height of a ball thrown in the air b) the temperature increasing steadily each hour c) the growth of bacteria doubling each hour

Explanation:

• Linear regression is used for linear relationships.
• For option A, the height of a ball thrown in the air follows a quadratic (parabolic) path (due to the effect of gravity, \(h(t)= - \frac{1}{2}gt^{2}+v_{0}t + h_{0}\), where \(g\) is the acceleration due to gravity, \(v_{0}\) is the initial velocity and \(h_{0}\) is the initial height), so it is not linear.
• For option B, if the temperature is increasing steadily each hour, the relationship between time \(t\) (in hours) and temperature \(T\) can be modeled as \(T = mt + b\) (where \(m\) is the rate of increase and \(b\) is the initial temperature), which is a linear relationship.
• For option C, the growth of bacteria doubling each hour is an exponential relationship (\(N = N_{0}\times2^{t}\), where \(N_{0}\) is the initial number of bacteria and \(t\) is the number of hours).

Answer:

B. The temperature increasing steadily each hour