The Economist magazine9 developed a quality-oflife index for nations as the predicted value obtained by regressing an average of life-satisfaction scores from several surveys on gross domestic product (GDP, per capita, in dollars), life expectancy (in years), an index of political freedom (from 1 = completely free to 7 = unfree), the percentage unemployed, the divorce rate (on a scale of 1 for lowest rates to 5 for highest), latitude (to distinguish between warmer and cold climes), a political stability measure, gender equality defined as the ratio of average male and female earnings, and community life (1 if country has high rate of church attendance or trade union membership, 0 otherwise). Table 11.23 shows results of the model fit for 74 countries, for which the multiple correlation is 0.92.

The study used the prediction equation to predict the quality of life for 111 nations.

The top 10 ranks were for Ireland, Switzerland, Norway, Luxembourg, Sweden, Australia, Iceland, Italy, Denmark, and Spain. Other ranks included 13 for the United States, 14 for Canada, 15 for New Zealand, 16 for the Netherlands, and 29 for the United Kingdom.

(a) Which variables would you expect to have negative effects on quality of life? Is this supported by the results?

(b) The study states that by itself “GDP explains more than 50% of the variation in life satisfaction.” How does this relate to a summary measure of association?

(c) The study reported that “Using so-called Beta coefficients from the regression to derive the weights of the various factors, life expectancy and GDP were the most important.” Explain what was meant by this.

(d) Although GDP seems to be an important predictor, in a bivariate sense and a partial sense, Table 11.23 reports a very small coefficient, 0.00003.Why do you think this is?

(e) The study mentioned other explanatory variables that were not included because they provided no further predictive power. For example, the study stated that education seemed to have an effect mainly through its effects on other variables in the model, such asGDP, life expectancy, and political freedom. Does this mean there is no association between education and quality of life? Explain.

TABLE 11.23 Coefficient Standard Error t Statistic Constant 2.796 0.789 3.54 GDP per person 0.00003 0.00001 3.52 Life expectancy 0.045 0.011 4.23 Political freedom −0.105 0.056 −1.87 Unemployment −0.022 0.010 −2.21 Divorce rate −0.188 0.064 −2.93 Latitude −1.353 0.469 −2.89 Political stability 0.152 0.052 2.92 Gender equality 0.742 0.543 1.37 Community life 0.386 0.124 3.13