In this picture and the others that follow the rate of economic growth has been adjusted for initial income: the variable on the vertical axis is that part of economic growth that is not explained by the country’s initial stage of development, obtained from a regression of growth during 1965-1998 on initial GNP per capita (i.e., in 1965) as well as the share of natural capital in national wealth. The correlation between economic growth on the vertical axis and the variable shown on the horizontal axis, in this case investment, is measured by the Spearman rank correlation coefficient, r. This measure is less sensitive to outliers than the more commonly used Pearson correlation coefficient. 

All the data underlying this picture and the ones that follow are obtained from the World Bank. 

For more on the relationship between investment and growth, see my recent paper "Natural resources and economic growth: The role of investment" with Gylfi Zoega and the associated slide show

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