Meaning of Min/Max Accuracy of a regression model I'm trying to measure the accuracy of some linear regression models I fitted in R. I ran into this page offering a technique called Min_Max Accuracy which is explained as:
Min_Max Accuracy => mean(min(actual, predicted)/max(actual, predicted))

and in R:
min_max_accuracy <- mean(apply(actuals_preds, 1, min) / apply(actuals_preds, 1, max))  

and actuals_pred is derived from this:
set.seed(100)  # setting seed to reproduce results of random sampling
trainingRowIndex <- sample(1:nrow(cars), 0.8*nrow(cars))  # row indices for training data
trainingData <- cars[trainingRowIndex, ]  # model training data
testData  <- cars[-trainingRowIndex, ] 
lmMod <- lm(dist ~ speed, data=trainingData)  # build the model
distPred <- predict(lmMod, testData)  # predict distance
actuals_preds <- data.frame(cbind(actuals=testData$dist, predicteds=distPred))

However, I can not understand what is Min_Max Accuracy representing. Could you please give me a hint of what it stands for? and is there any name synonym for this concept that I can look it up? Thanks 
 A: Let's break down the code:
apply(actuals_preds, 1, min)

Takes, for each row, the minimum of the prediction and the result. Similarly, 
apply(actuals_preds, 1, max)

takes the maximum.
Suppose the test outcomes are $y_1, \ldots, y_n$, and the predictions are $\hat{y}_1, \ldots, \hat{y}_n$. For any $i$, there are two cases:
The first case is $\hat{y}_i = y_i - \epsilon_i$ for some $\epsilon_i \geq 0$. In this case, row $i$ will add to the mean, the term 
\begin{equation}
\frac{y_i - \epsilon_i}{y_i} = 1 - \frac{\epsilon_i}{y_i}.
\end{equation}
The second case is $\hat{y}_i = y_i + \epsilon_i$ for some $\epsilon_i \geq 0$. In this case, row $i$ will add to the mean, the term 
\begin{equation}
\frac{y_i}{y_i + \epsilon_i} \sim 1 - \frac{\epsilon_i}{y_i}.
\end{equation}
where the approximation holds for $\epsilon_i < y_i$ due to the series expansion of $\frac{1}{1 + x}$.
Finally
mean(min(actual, predicted)/max(actual, predicted))

takes the average of all these terms, obviously. 
The better the prediction, the higher it will be (approx. 1 for a nearly perfect prediction).
A: MinMax tells you how far the model's prediction is off. For a perfect model, this measure is 1.0. The lower the measure, the worse the model, based on out-of-sample performance. 
Just look at the formula  and how it's implemented in R. If predict (the column predicteds in your data frame) exactly equals actual (actuals) for every instance of the test set, the row minimum would be the same as the row maximum, so the ratio would be 1.0 for all rows. 
If your model is terrible, sometimes its prediction is too high, other time too low, the min/max ratio would be much less than 1.0. So the average of that would be less than 1.0. 
A: Actuals and predict both are in same dataset. Min_Max_accuracy will find out accuracy rate of each row. it can be considered accuracy rate of the model. it would less than zero like .69034, then accuracy percentage is 69%. 
