Definetely, it is reasonable. You may assume that a pet as a companionship will help the elderly feel more comfortable and therefore, happy. There are a few problems tough:
There is no practical way of meassuring 'happiness'.
Sometimes, the correlations of two factors may be a coincidence. Scientist should always consider this when they try to claim something byusing some backup logic, like we did.
Even tough the statement makes some sense, you need to be aware that maybe is not completly positively correlated. Maybe having 20 more pets does not make an elderly happy if it alredy had 1 or 2.
