Exercise

# Simpson's paradox in action

A mild version of Simpson's paradox can be observed in the MarioKart auction data. Consider the relationship between the final auction price and the length of the auction. It seems reasonable to assume that longer auctions would result in higher prices, since—other things being equal—a longer auction gives more bidders more time to see the auction and bid on the item.

However, a simple linear regression model reveals the opposite: longer auctions are associated with lower final prices. The problem is that all other things are *not* equal. In this case, the new MarioKarts—which people pay a premium for—were mostly sold in one-day auctions, while a plurality of the used MarioKarts were sold in the standard seven-day auctions.

Our simple linear regression model is misleading, in that it suggests a negative relationship between final auction price and duration. However, *for the used* MarioKarts, the relationship is positive.

Instructions

**100 XP**

The object `slr`

is already defined for you.

- Fit a simple linear regression model for final auction price (
`totalPr`

) as a function of duration (`duration`

). - Use
`aes()`

to add a color aesthetic that's mapped to the condition variable to the`slr`

object, which is the plot shown at right.