Table 4.5 shows the growth of the population of Tennessee

Chapter 4, Problem 41

(choose chapter or problem)

Table 4.5 shows the growth of the population of Tennessee from the 1850 census to the 1910 census. The table gives the population growth beyond the baseline number from the 1840 census, which was 829,210. t p 0 20 100 30 40 50 150 200 250 300 350 50 Time (days) Number of flies 10 r r s Table 4.5 Population Growth of Tennessee Years since Growth Beyond 1840 1840 Population 10 173,507 20 280,591 30 429,310 40 713,149 50 938,308 60 1,191,406 70 1,355,579 Source: Bureau of the Census, U.S. Chamber of Commerce (a) Find the logistic regression for the data. (b) Graph the data in a scatter plot and superimpose the regression curve. (c) Use the regression equation to predict the Tennessee population in the 1920 census. Be sure to add the baseline 1840 number. (The actual 1920 census value was 2,337,885.) (d) In what year during the period was the Tennessee population growing the fastest? What significant behavior does the graph of the regression equation exhibit at that point? (e) What does the regression equation indicate about the population of Tennessee in the long run? (f) Writing to Learn In fact, the population of Tennessee had already passed the long-run value predicted by this regression curve by 1930. By 2000 it had surpassed the prediction by more than 3 million people! What historical circumstances could have made the early regression so unreliable?