Question: An engineer in charge of process improvement wants to study the relationship between the total number of hours of training that an operator has received (X = independent variable) and the time in minutes that the operator requires to produce a component (Y = dependent variable). She collects the following data:

Xi Yi

1 8

2 6

4 4

Based on her previous studies and experience, the engineer believes that the relationship between Y and X is as follows:

\[\hat{y}={{b}_{0}}+{{b}_{1}}\left( \frac{1}{x} \right)\]

Find the values of b₀ and b₁ using the method used in regression (that is. minimizing the sum of squares of prediction errors) and predict the time in minutes required by the operator to produce the component, after receiving 3 hours of training.