The graph is from recently published research by Cornell political scientist Peter Enns.  The measure of public support for being tough on crime comes from averaging together 33 different questions about crime policy that have been asked repeatedly during this period.

As the graph indicates, there is a strong correlation: the more the public wants to get tough on crime, the more the incarceration rate increases.  Enns shows that this correlation persists even after accounting for the crime rate and several other factors.  Enns also shows that public opinion appears to be driving the incarceration rate, and not vice versa.  He concludes:

The public’s rising punitiveness appears to be a fundamental determinant of the incarceration rate. In fact, if instead of becoming more punitive, the public’s support for being tough on crime had remained constant since the mid-1970s, the results suggest that there would be about 20% fewer people incarcerated today.

You can read his research here, and Enns’ discussion of this research here.