So another way of thinking is this notion of log odds. So if you take exponential of the coefficients, so for example, you take the exponential of the coefficients of serviced, it is 1.4. That means, if the clock is not serviced versus it is serviced, your log odds drops to 14 percent, everything else remaining constant. If a clock is not service versus it is serviced, the ratio of your winning to your losing probability drops with 14 percent. That's interesting. Price has a log odds of minus 0.998, e to the power of minus 0.998. You can see that, there it is. So to adjust for a clock which is serviced, think about it. I must adjust it so that that 14 percent drop is compensated by the extra price I bid. A little bit of math will show you that to retain the same log odds, I must increase the price by $1,000. Why? One thousand times the coefficient on price is 0.002. So 1,000 times 0.002 is two and two will knock out minus 1.9. In plain language, it means and I'm excited, that if a clock is not serviced, I had to pay $1,000 more to have the same log odds of winning. That's one way, and I ask myself is that true? That means clocks that are serviced are worth 1,000 bucks. Maybe. I've just shown you the error matrix, and I've shown you the prediction. I said and my overall error rate is 23 percent. You say, "Is this good or not?" Well, there is a basic test that we do. One test is, let's say I knew nothing and I said I will either lose the bid always or I will win the bid always. If I did that and chose the higher of the two probabilities, that's called the base case. Obviously, I will choose saying that I will lose all my auctions. If I'd said that, I would be right 65.45 percent of the time. That means, that's because I lost 65.45 percent of my auctions. So without any model, without asking anybody, without any data, with this kind of a model, I would have lost 65.45 percent. So without all this logic and all that, the best guess I can make is I'm going to lose. Now, what the logic model is doing it is improving the accuracy of your prediction to 76.4 percent over the base case. So base case again is just bidding on head all the time or tail all the time. Whereas the logic model sometimes bids on head sometimes bids on tail, which is obviously going to do better but how much better? What this model is doing is it is doing better 76.4 percent, which is one minus 23.6 percent. Which is the error, you saw that. So on top of it, it's predicting half the time that I will bid correctly and I'm quite excited about it. Of course, I bid and I won all of my bids recently and I got a yea big Atmos clock on my table which is running, it's going a little slow but I have to make sure to tune it so it runs fast. So I'm sorry we're talking about model performance and not clock performance. So just to summarize what we have done is I have taken this notion of linear regression. We've applied it to a categorical variable which is win or loss. You can actually do it from multiple categories also. It can be used as we saw with the whole lot of sample. So obviously it can be used for prediction, to predict whether you will win an auction, or whether the car is a sports car, or whatever it is. I'm going to give you an exercise. The relationship between the independent and the dependent variables, predictor variables and the response variables are through this function called the logic function. Everything else remains the same. So I'm going to give you a fairly exciting exercise for you to try. Remember the Boston Housing dataset? Don't partition the data because the data is not too big. Run the logistics regression to predict whether the house or the tract bounds the Charles River. So that's a zero or one variable, right? So use only two variables to predict the price of the house and the degree of industrialization in that particular area. So use only two variables medv and indus. Check your coefficients, this is what you should get and the error matrix should be 6.9 percent. So basically, just the prize and the degree of industrialization is telling you whether the house is adjoining Charles River or Northern Boston.
