I don't think there is any data to show that BC increases a consoles sales substantially. The GBA, Wii U, and 3DS were BC, but both sold less than their predecessors. The PS Vita had BC for digital titles and sold substantially less than the PSP. The PS3 initially had BC and sold very poorly initially. In fact, the PS3 had PS1 BC for all PS3 units, and still sold less than the PS1 did. 

Then there are consoles, such as the PS4 and the Switch, which are some of the best selling consoles of all time without BC. There simply doesn't seem to be a correlation between BC and sales. 

People always talk about previous consoles performance helping/hurting sales but they have almost no affect on how much a new console will sell.

PS2-157m to PS3-87m to PS4-117m

XB-25m to 360-86m to XBO-50m

DS-155m to 3DS-76m

PSP-81m to Vita-16m

GC-22m to Wii-101m to Wii U-14m

A console sells based on its own merits, not on how well a console that released 4-7 years earlier did.