Hi!
I have enabled the statistics for you via the back-end access. After pressing the button, the page should reload and automatically save the option. I guess there might have been a script conflict there, now it should be enabled.
The analytics integration is to track the search queries as pageviews when ajax search is used. When enabled, the plugin will send a page view when a live search is successfully completed and the results have been displayed. The results page is simply tracked by google analytics as a pageview automatically, without this option active.