What is the relationship between bandwidth and data rate? I know bandwidth is usually just the difference betweent he highest and lowest frequencies but then how does data rate come into play? What if you increase your bandwidth, what would be the change in data rate? Equal to whatever change you make?

One simple analogy can explain the things. We can consider the bandwidth as the diameter of the water pipe. A larger pipe can carry a larger volume of water, and hence more water can be delivered between two points with larger pipe. How large is the pipe (bandwidth) determines maximum quantity of water (data) flows at a particular time. So more the bandwidth more data can be transferred between two nodes. So increasing bandwidth can increase data transfer rate. Data transfer rate can vary due to distance between two nodes, efficiency of medium used etc. So higher bandwidth does not always guarantee higher data transfer rate. So fundamentally they are not related to each other. Data transfer can be considered as consumption of bandwidth. 

