After a successful business career, you decide to retire early

After a successful business career, you decide to retire early and go into car racing, not as a driver yourself, but as an entrepreneur. You buy a car and a workshop and hire a celebrity driver who tells you that the key to winning is the car’s transmission. “The faster I can shift those gears,” he says, “the more power goes to the wheels.” You therefore decide to hire some engineering developers to take transmissions apart, adjust and modify them, and reassemble them as a custom transmission that only your car has. At the end of each season, you negotiate next season’s contract with your driver, depending on the winnings he brought in during the season that has just finished. You also pay bonuses in the current season to your other employees dependent on the winnings during the same season.

You love the sport, as does everyone in your team, and have enough savings that you don’t need to make a profit, but decide to hire an accountant to take a look at your financial performance to date (currently the end of your fifth season):

Here are the comments of the accountant. For each comment, say whether you agree and fit a linear model if possible. If you can help the accountant by estimating something using your linear model, then do so.

a) “Winnings are an unpredictable fraction of total income. It’s tough to estimate what fraction it’s going to be next season.”

b) “Your profits don’t seem to be related to your winnings.”

c) “The contract you have with your driver seems to be closely related to the winnings. It would be good to have a measure of how close.”

d) “The amounts you pay your mechanics and developers also seem to be closely related to your winnings, but some of them told me they are concerned with how much they would get if winnings dropped to $0.5m one year.”

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