3.1.3. Bi-Variate Regressions

Table 1 presents an overview of the standardized bi-variate Ordinary Least Squares (OLS) regression coefficients and statistical significance between household size (as a dependent variable) and urban-rural typology, carbon and energy footprints, and income per capita (as independent variables) across EU countries. Table 1 confirms a strong negative relationship between household size and per capita energy and carbon footprints within countries. The EU coefficients amount to −0.17 and −0.20 for carbon and energy footprints, respectively. Across countries, the coefficients vary between −0.11 (in Romania) and −0.39 (in Luxembourg) for carbon, and between −0.12 (in Romania) and −0.44 (in Czech Republic) for energy.


**Table 1.** Standardized bi-variate regression coefficients (can be interpreted as pairwise correlation coefficients) between household size and other variables by EU country.

Note: \* *p* < 0.05, \*\* *p* < 0.01, \*\*\* *p* < 0.001. The variables densely populated (*DENSE*) and sparsely populated (*SPARSE*) are dummies. In the context of this table, *HHSIZE* can be interpreted as a dependent variable, and the rest of the variables—as independent variables. Household weights provided by the HBS have been applied.

Furthermore, densely populated contexts (cities) are associated with smaller household sizes, and sparsely populated rural contexts – with larger household sizes in most EU countries (Table 1). The lowest regression coefficients between household size and densely populated context are found in Poland (−0.19) and Germany (−0.18). The opposite is true for sparsely populated areas, with the highest significant coefficient between household size and sparsely populated context found in Poland (0.14). Portugal shows an exceptional trend, being the only country with a negative and significant coefficient for household size and sparsely populated context.

While we note substantial inter-country differences, household dynamics should clearly be analyzed controlling for other socio-demographic trends (such as income and population density) [16]. For example, the analysis confirms a strong negative relationship between income and household size across all EU countries—suggesting an association between lower household sizes and higher incomes—with a coefficient amounting to −0.21 for the EU.
