In the literature, apart from Gross Domestic Product (GDP) per Capita, a number of factors have been identified as non-income determinants of health care expenditure. Most studies linking health care expenditure to income and other important variables have originated in advanced countries. This study considers a linear regression model via shrinkage methods to identify key predictors of health care expenditure in Africa. Shrinkage is a process of estimation where a subset of redundant predictor variables is discarded, leaving only important ones in the linear regression model. The study was based on 42 African countries for the year 2012 and GDP per Capita, Consumer Price Index (CPI), Exchange Rate (EXC), Corruption Perception Index (COP), and Population Density (POP) were identified as key predictors of Health Expenditure per Capita (HEC). A major finding identified the Elastic net model as critical in accurately estimating HEC in Africa.