Final answer:
Robert's most advantageous filing status is Head of Household.
Step-by-step explanation:
If Robert Smith is unmarried, lives alone, and paid more than half of the cost of keeping up his parents' home, and his parents are his dependents for tax purposes, then his most advantageous filing status would be Head of Household.
Head of Household is a filing status that is available to individuals who are unmarried, but provide financial support for a qualifying person, such as a parent. To qualify as Head of Household, Robert must meet certain requirements, including paying more than half of the cost of keeping up his parents' home and having his parents listed as dependents on his tax return.
This filing status offers several benefits, including a higher standard deduction and lower tax rates compared to filing as Single. It is important for Robert to carefully review the requirements and consult with a tax professional or the IRS to ensure that he meets all the necessary criteria to claim the Head of Household filing status.