Is multiple regression the best method of statistical analysis

What are you going to use for a control group? To compute the probability of falling, you need some reference where people didn't fall. Do you have that? In a normal experimental setup, you would measure your three independent variables for a large population, then follow them and see where the falls occur. The other option would be to look at every patient checking out of the hospital, collecting their scores and noting if they fell or not. (This is not as good IMO because they were in the hospital for some reason so they don't represent the general population well.) Then you can use an ANOVA and out pops the value of your independent variables. You are only looking at the positive events (which is a bad statistical error) with no control so I don't see how you can find correlations. You also need to know if your independent variables are really independent. Do lowered motor abilities and cognitive abilities coincide?

Given what you have, what I would do is first pull a large set of data for fall risk score, motor ability score and cognitive ability for a normal population of people. I would compare those against each other to see if the variables correlate at all and I would generate histograms for each variable. I'd plot 2-D plots showing each of the three variables against the other two then plot the fall data on the same plot to see if the fall data skews to one side. If you have to do a mathmatical test, you could assume that each data point in your large group represents a non-fall and go back to an ANOVA. I don't think this is rigorous but I don't see how you could do better.