# Question: The table shows the world population size in billions since

The table shows the world population size (in billions) since 1900.

a. Let x denote the number of years since 1900. The exponential regression model fitted to y = population size and x gives = 1.424 × 1.014x. Show that the predicted population sizes are 1.42 billion in 1900 and 6.57 billion in 2010.

b. Explain why the fit of the model corresponds to a rate of growth rate of 1.4% per year.

c. For this model fit, explain why the predicted population size

(i) Doubles after 50 years and

(ii) Quadruples after 100 years.

d. The correlation equals 0.961 between the population size and the year number and it equals 0.991 between the log of the population size and the year number. What does this suggest about whether the straight-line regression model or the exponential regression model is more appropriate for these data?

a. Let x denote the number of years since 1900. The exponential regression model fitted to y = population size and x gives = 1.424 × 1.014x. Show that the predicted population sizes are 1.42 billion in 1900 and 6.57 billion in 2010.

b. Explain why the fit of the model corresponds to a rate of growth rate of 1.4% per year.

c. For this model fit, explain why the predicted population size

(i) Doubles after 50 years and

(ii) Quadruples after 100 years.

d. The correlation equals 0.961 between the population size and the year number and it equals 0.991 between the log of the population size and the year number. What does this suggest about whether the straight-line regression model or the exponential regression model is more appropriate for these data?

**View Solution:**## Answer to relevant Questions

Match each of the following scatter-plots to the description of its regression and correlation. The plots are the same except for a single point. Justify your answer for each scatter-plot. a. r = -0.46 = 142 - 15.6x b. r = ...For the High School Female Athletes data set on the text CD, conduct a regression analysis using the time for the 40-yard dash as the response variable and weight as the explanatory variable. Prepare a two-page report, ...The statistician George Box, who had an illustrious academic career at the University of Wisconsin, is often quoted as saying, “All models are wrong, but some models are useful.” Why do you think that, in practice, a. ...For a study of University of Georgia female athletes, the prediction equation relating y = total body weight (in pounds) to x1 = height (in inches) and x2 = percent body fat is = -121 + 3.50 x1 + 1.35x2. a. Find the ...For the Georgia Student Survey file on the text CD, the prediction equation relating y = college GPA to x1 = high school GPA and x2 = study time (hours per day), is = 1.13 + 0.643x1 + 0.0078x2. a. Find the predicted college ...Post your question