Problem 4b in Section 3.1

Data from problem 4b

In the following data, V represents a mean walking velocity and P represents the population size. We wish to know if we can predict the population size P by observing how fast people walk. Plot the data. What kind of a relationship is suggested? Test the following models by plotting the appropriate transformed data.

b. P = a ln V

For Problems 1-6, find a model using the least-squares criterion either on the data or on the transformed data (as appropriate). Compare your results with the graphical fits obtained in the problem set 3.1 by computing the deviations, the maximum absolute deviation, and the sum of the squared deviations for each model. Find a bound on c_max if the model was fit using the least-squares criterion.