Whereas Mississippi and Yellowstone both represent the nature of N-America, so do they have something more in common? The answer is yes, if we look below the crust and the tectonic plate. It can be reasoned that a main lower mantle convection rolls division line is found underneath the continent, parallel to the pair of convection rolls shaping the Atlantic Ocean. A lower mantle convection roll spans 30° from east to west, presuming that the height to width ration is close to 1:1.
The resulting pattern of convection rolls includes the upper mantle counterpart of the main division lines, comprising the Mississippi line. Mississippi follows that division line remarkably closely, and the point where it crosses the lower mantle convection rolls division line is probably geologically the most central of the whole continent. Let us look at this on a map:
First, we can see how Mississippi follows a main division line of upper layers of the mantle. About 55 million years ago, the N-Atlantic Ocean was opening up, but parallel forces are at work along this large scale division line below N-America, shown here. N-America did not split apart, obviously, but when the partly divided (stretched) area from that time reached the point where Yellowstone is located now, the Columbian River Flood Basalt formed with countless eruptions, mainly about 16 million years ago, as can be learned about here: https://en.wikipedia.org/wiki/Columbia_River_Basalt_Group
The N-S axis met with at the site of Yellowstone can be shown on another map:
The N-S axis is a large scale feature, of the same scale as forms the southern half of the Mid-Atlantic Ridge south of equator. The convection found within the asthenosphere below 120 km can then send magma into the crust, resulting in melting processes leading to geothermal and eventually volcanic activity at the location of Yellowstone. The volcanic fissures of the Columbian Flood Basalt are oriented in line with the convection rolls, the same direction as that of the Mississippi river at similar latitudes.
So now you see how the Mississippi River and Yellowstone are connected 😉