If the Holy Spirit is God, and is given to us who have faced up to the sins and repented, there must be evidence that the Holy Spirit is staying inside us. What we believe in the Holy Spirit is more valuable when it is proven through our experience.
Let's suppose I have a timetable that records the departure time of the bus to the city I want to visit. Although the timetable is true and accurate, it doesn't take me to the city.
The information in the timetable becomes valuable eventually only when I take the bus to the city at the time and go through it myself.
Likewise many Christians are only interested in believing in the truth rather than experiencing it. We must establish a solid foundation for the truth shown in the Bible. But we need to see the truth of the Bible in our life by experiencing the Words of truth.
The first evidence of the Holy Spirit's staying inside us is a new desire to know Jesus Christ. If we don't have a desire to know Christ better and deeper, the Holy Spirit will not be staying in us any more, but either disappearing or worrying.
Revised from Charles M. Price, 'Real Christians(1987)'
(Source: A story like sunlight)