{GGally} library by R is what would help you. Using it you can create multi-parameter scatterplot matrices. For examples in my case various environmental parameters (volcanic areas, depth, sediment thickness etc, divided by 25 bathymetrics profiles crossing 4 tectonics plates). You can look at the script here:
Code R script to plot scatterplot matrix to perform correlation a...
No, this is correlation matrix, not regression lines. The lines show dependencies They show dependencies between the observation points and the environmental variables. Methodology was the following: I had bathymetric profiles across the trench with profiles consisting of 518 points: you can see their numbers on the bottom (in some cases they are about 300 because not all profiles cross four plates).
So, on the X-axis (horizontal) we can see the points. On the Y-axis (vertical) - environmental factors (tectonic, geomorphology etc) with their scale. For example, bathymetric depths (central right row) values -10.000, -6.000 etc. Because the profiles cross 4 tectonic plates I coloured them in four colours: rose, purple, orange and green. So, we can see the relationship between the factors across the observation points (what are the angles steepness across the lines, what are the depths, how thick is sediment layers). It is not regression analysis, it is correlation matrix.
But your parameters will be different, of course. This is just my study case.