The phrase "to support that conclusion" means to provide evidence, reasons, or facts that help strengthen or prove the idea or decision that has been made or reached. Full definition
The second set of data supports a conclusion that entrepreneurship faces a major challenge. (inc.com)
To accept «as is,» the experimental design needs to be sound and the data need to be clean and accurate enough to support the conclusions drawn. (sciencemag.org)
I have a couple of questions, one being where the paper supports the conclusion in the related news releases about the polar bear's evolution being a slow process. (dotearth.blogs.nytimes.com)