In Problems, construct a scatterplot of the given data. Is there a trend in the data...

In Problems, construct a scatterplot of the given data. Is there a trend in the data? Are any of the data points outliers? Construct a divided difference table. Is smoothing with a low-order polynomial appropriate? If so, choose an appropriate polynomial and fit using the least-squares criterion of best fit. Analyze the goodness of fit by examining appropriate indicators and graphing the model, the data points, and the deviations.

The following data represent the “pace of life” data (see Problem 1, Section 4.1). P is the population and V is the mean velocity in feet per second over a 50-ft course.

REFERENCE:

In 1976,Marc and Helen Bornstein studied the pace of life.2 To see if life becomes more hectic as the size of the city becomes larger, they systematically observed the mean time required for pedestrians to walk 50 feet on the main streets of their cities and towns. In Table 4.5, we present some of the data they collected. The variable P represents the population of the town or city, and the variable V represents the mean velocity of pedestrians walking the 50 feet. Problems are based on the data in Table 4.5.

4.1.1 : Fit the model V = CP^a to the “pace of life” data in Table 4.5. Use the transformation log V = a log P + logC. Plot log V versus log P. Does the relationship seem reasonable?

a. Make a table of log P versus log V.

b. Construct a scatterplot of your log–log data.

c. Eyeball a line l onto your scatterplot.

d. Estimate the slope and the intercept.

e. Find the linear equation that relates log V and log P.

f. Find the equation of the form V = CP^a that expresses V in terms of P.