The quantitative relationships between radon gas concentration, the surface-deposited activities of various radon progeny, the airborne radon progeny dose rate, and various residential environmental factors were investigated through a Monte Carlo simulation study based on the extended Jacobi room model. Airborne dose rates were calculated from the unattached and attached potential alpha-energy concentrations (PAECs) using two dosimetric models. Surface-deposited 218Po and 214Po were significantly correlated with radon concentration, PAECs, and airborne dose rate (p-values <0.0001) in both non-smoking and smoking environments. However, in non-smoking environments, the deposited radon progeny were not highly correlated to the attached PAEC. In multiple linear regression analysis, natural logarithm transformation was performed for airborne dose rate as a dependent variable, as well as for radon and deposited 218Po and 214Po as predictors. In non-smoking environments, after adjusting for the effect of radon, deposited 214Po was a significant positive predictor for one dose model (RR 1.46, 95% CI 1.27–1.67), while deposited 218Po was a negative predictor for the other dose model (RR 0.90, 95% CI 0.83–0.98). In smoking environments, after adjusting for radon and room size, deposited 218Po was a significant positive predictor for one dose model (RR 1.10, 95% CI 1.02–1.19), while a significant negative predictor for the other model (RR 0.90, 95% CI 0.85–0.95). After adjusting for radon and deposited 218Po, significant increases of 1.14 (95% CI 1.03–1.27) and 1.13 (95% CI 1.05–1.22) in the mean dose rates were found for large room sizes relative to small room sizes in the different dose models.