Regression analysis has been used to characterize the relationship between an exposure dose and the incidence of an adverse health effect such as cancer. However, the regression rarely describes the true relationship due to uncertainties in dose-response data and relationships. Therefore, a method is developed to perform dose-response assessments by a fuzzy linear regression which explicitly exhibit these uncertainties. This method is applied to define the relationship between a particular nitrate dose to humans and its corresponding cancer risk.

A multiple regression method (MRM) is used for the first time with Ozone Monitoring Instrument (OMI) and Moderate Resolution Imaging Spectroradiometer (MODIS) data to estimate formaldehyde (HCHO) column over Asia in two categorized areas: (1) anthropogenic areas in East Asia (east-central China, Beijing, Seoul, and Tokyo) and (2) biogenic and pyrogenic areas (Indochina and South Borneo). In order to determine the multiple regression equations (MREs) for each study area, monthly mean and daily values of Nitrogen dioxide (NO2) level, land surface temperature (LST), enhanced vegetation index (EVI), and fire radiative power (FRP) from 2005 to 2006 were used as independent variable candidates and monthly mean and daily HCHO measured by OMI (HCHOOMI) for the same period was used as the dependent variable. The MREs estimated HCHO (HCHOMRM) with inputs of independent variable data for from 2005 to 2006 whereas they estimated HCHO (HCHOVAL) with inputs of independent variable data in 2007. The agreement between HCHOOMI and HCHOVAL is comparable with that between HCHOOMI and HCHOMRM in both monthly and daily scale. The average correlation coefficient, slope, mean bias, mean absolute error, root mean square error, and percent difference between monthly HCHOOMI and monthly HCHOVAL (between daily HCHOOMI and daily HCHOMRM) are 0.89 (0.58), 0.77 (0.34),-0.82 × 10 15 molecules cm-2 (-0.91 × 10 15 molecules cm-2), 1.28 × 10 15 molecules cm-2 (3.01 × 10 15 molecules cm-2), 1.75 × 10 15 molecules cm-2 (4.32 × 10 15 molecules cm-2), 10.2% (24.1%). MRM can be a useful tool to provide HCHO in certain area in Asia.