Plot the scatter diagram using the crude birth rate as the Y variable and GDP per capita as the X variable from the data given in given Problem.
(a) Fit a least-squares regression line and compute T.
(b) Try a transformation on X and recompute r. Did it increase, and if so, why?
Problem
The following table contains data from 17 countries. These countries are a systematic sample from twice this number of countries that had a population > 30 million people in 1998 and had complete data. The data were taken from the US. Bureau of the Census, Statistical Abstracts of the United States; 1998, 118th ed., Washington, DC. It consists of the crude birth rate (CBR) or the total number of births divided by the total population in 1998, life expectancy (LifeExp) from birth in years for the overall population, and gross domestic product (GDP) per capita for 1995. The GDP has been adjusted and then converted to U.S. dollars.
Country CBR LifeExp GDP
Argentina 20 74.5 7,909
Brazil 20.9 64.4 4,080
Canada 12.1 79.2 19,000
Colombia 24.9 70.1 2,107
Egypt 27.3 62.1 746
France 11.7 78.5 26,290
India 25.9 62.9 348
Iran 31.4 68.3 2,449
Japan 10.3 80.0 41,160
Mexico 25.5 71.6 2,521
Pakistan 34.4 59.1 482
Poland 9.8 72.8 5,404
S. Africa 26.4 55.7 3,185
Tanzania 40.8 46.4 134
Thailand 16.8 69.0 2,806
United Kindgom 12.0 77.2 19,020
United States 14.4 76.1 27,550
(a) State which model the data in the table follows.
(b) Plot the scatter diagram when X = life expectancy and Y = crude birth rate and fit a regression line.
(c) Does the data appear to follow a straight line?
(d) If life expectancy increased by 10 years, what do you expect to happen to the crude birth rate?
(e) Test that Ho : β = 0. If you test that p = 0, will you get the same P value?