[HashiriyaR32]

Spoiler for EP6, ID:

The corresponding ID manga volume for the AE86 vs FD race is volume 2. Yui's Subaru Vivio RX-R is a BLATANT reference to Bunta Fujiwara's Impreza WRX STi Type R (GC8V). Kagami's outburst ("What's with the Initial D-like driving?!?!") made the parody extremely obvious.
Here's another tidbit on the Vivio. It's the only K-car to have a supercharged engine (all other K-cars I know, such as the Cappuccino, i, Wagon R, Copen are powered by turbocharged engines). I'm very surprised the producers didn't add in a supercharger whine for when doing the interior shots for the Vivio.