We're examining "salesperson cost per sale," where cost is just what the agent is paid in compensation. In other words, our target variable is the ratio of (salesperson pay)/(count of sales).
I'm doing a k-dimensional linear regression, where one feature happens to be the sum of three other features: regular pay + overtime pay + commission pay = total pay. Other features are included, like number of sales calls, average sale call time, total time working, etc.
RegPay...OTPay...Commission...TotalPay...AverageCallTime...KthFeature...CostPerSale 7173.....119.....3681.........10974......4530..............511..........3.96 . . . 8122.....348.....2267.........10737......3367..............693..........4.13
Interestingly, the RegPay, OTPay, and Commission features are the three most positively correlated with the CostPerSale target, but the TotalPay feature is the most negatively correlated.
How can this be possible?