Our living room is 15 wide by 16 long, which way should we run the hardwood to make the room look bigger? I don't know if the colors matter but just in case it does, the walls are a beige color and the hardwood is a chocolate brown color.
Rule of thumb is that hardwood is installed parallel to the longest wall to create the largest feel. Since your room is almost square, I would be tempted to install it parallel to the door or entry. The other consideration is how much subflooring is under the new floor and what kind of floor you are installing. If you are going to install 3/4" nail down over a single 3/4" subfloor, I would run it perpendicular to the floor joists and be sure to nail into the joists. If you are using a staple down, glue down or click lock, the choice is more arbitrary. Yet another factor is the subfloor thickness and clearance to doors and adjoining floors. If you are using a thinner flooring, You should have the basic 3/4" sheathing with at least 3/8" subfloor installed over the 3/4". Paper between all wood layers to prevent squeaking.
This question is possibly subjective. But in my study, I chose to run my wood flooring diagonal; the same diagonal that you are looking along when you peer into the study from its doorway. I felt that this helped to draw the eye to the farthest corner. I put a fancy chair & potted plant in that corner, to act as the room's conceptual centerpiece.
I am not an interior decorator or anything; this is just my opinion.