FULL SCREEN PRINTER VERSION NEXT Chapter 11, Section 11.5, Problem 32a One measu

Question

FULL SCREEN PRINTER VERSION NEXT Chapter 11, Section 11.5, Problem 32a One measure of the development of a country is the Human Development Index (HDI). Life expectancy, literacy, educational attainment, and gross domestic product per capita are combined into an index between 0 and 1, inclusive with 1 being the highest development. The United Nations Development Program reports values for 177 countries. We randomly selected fifteen countries, below the top twenty-five. Both HDI and the predictor variable x-Internet usage per 100 persons are obtained from their reports. Country Internet/100 HDI Bahrain 21.3 0.866 Poland 26.2 0.870 Uruguay 14.3 0.852 Bulgaria 20.6 0.824 Brazil 19.5 0.800 Ukraine 9.7 0.788 Dominican Republic 16.9 0.799 Moldova 9.6 0.708 India 5.5 0.619 Madagascar 0.5 0.533

Explanation / Answer

Back-up Theory

Let X = internet usage and Y = HDI

The regression model is X = + Y + , where is the error term, which is assumed to be Normally distributed with mean 0 and variance 2. Then,

Estimated Regression of X on Y is given by: xcap = a + by, where

b = Sxy/Syy and a = Xbar – b.Ybar…………………………....…………………….(1)

where

Xbar = (1/n)sum of xi over i = 1, 2, …., n; ………………………………………….(2)

Sxx = sum of (xi – Xbar)2 over i = 1, 2, …., n ………………………………………(3)

Ybar =(1/n)sum of yi over i= 1, 2, …., n;………………………………….………….(4)

Syy = sum of (yi – Ybar)2 over i = 1, 2, …., n ………………………………………(5)

Sxy = sum of {(xi – Xbar)(yi – Ybar)} over i = 1, 2, …., n……………………….…(6)

Estimated Regression of X on Y is given by: Y = a + bY

Calculations

n = 15

xbar = 9.953

ybar = 1.000

Sxy = 20.4008

Syy = 0.4177

a = - 22.7335

b = 49.0056

Estimated Regression of X on Y is given by: xcap = 49.01y – 22.73 ANSWER

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