Question

1. The OECD (Organization for Economic Cooperation and Development) consists of 20 advanced, industrialized countries. Based on these 20 cases, the regression equation relating X = percent of gross domestic product devoted to social expenditure and Y = child poverty rate is E(Y) = 22 – 1.3X. The values of X range from 2% (United States) to 16% (Denmark). The values of Y range from 2.8% (Finland) to 21.9% (United States). The correlation between X and Y is –0.79.
   1. Interpret the intercept and the slope coefficient.
   2. Find the predicted child poverty rates for the U.S. and Denmark
2. 3. Interpret the correlation.
   4. Use the correlation to find a common measure of model fit.

Answer 1

a) regression equation is

Y=22 - 1.3 X

Intercept = a = 22

When percent of gross domestic product devoted to social expenditure X=0 , child poverty rate is 22

Slope = b = when there is 1 unit change in X then decrease in child poverty rate by 1.3

B) US=2% , Denmark=16%

For US

Y^ = 22 - (1.3*2) = 19.4

For Denmark

Y^= 22 - (1.3*16) = 1.2

C) correlation = r = - 0.79

There is moderate negative correlation between percent of gross domestic product devoted to social expenditure X and child poverty rate Y

D) coefficient of determination = r² = ( -0.79 )² = 0.6241

62.41% of variation explained in child poverty rate is explained by percent of gross domestic product devoted to social expenditure .