Naming linear data or non-linear data is a bit misleading and wrong I would say. Instead, there is linear relation and non-linear relation between variables would be better and correct naming. It can easily be explained by example from real life.
* Non-linear relation: Any kind of relationship that is not linear can be put forward as an example (e.g. quadratic relation: y = intercept + x^2, square root relation: y = intercept + 6 * sqrt(x) etc.) Let's imagine a world where we are not aware of the free fall equation and we use ML to learn and predict it :). In that case (specific and simplified case), the algorithm would need to learn an equation in the following structures = v₀t + (1/2)gt², where t is our independent variable, s is our target or dependent variable and v₀, g would be our coefficients to be learned. In other words, you would want to predict free fall (distance or height) using time. In that fictional world, <PERSON>’s Law of Universal Gravitation (F = G * (M1 * M2) / r^2), Area of a circle (A = π * r^2) would also be a quadratic problem for ML. Linear functions do not meet the requirements of such cases unless you use some kind of transformation, let's say take the square root of r^2 from <PERSON>'s law or the square root of t^2 from free fall then use them in a linear function. 964
The most known example of non-linear real-life relation is a prediction of height using age. Height changes continuously, however, in different rates: until 13 gradually increases, between 13-18 significantly increases, between 18-25 slightly changes, and after 25 it does not change. Thus, it is impossible to fit it into a linear equation, because it is not dependent on a single coefficient or i.o.w. it does not fit into the formula height = intercept + b * age because coefficient (b) is not constant over time (age). Moreover, Graph, Tree, and other similar structures are also fitted into a non-linear relationship. In cases where the result is highly dependent on ifs, linear algorithms are useless because you cannot fit the relationship into y = a + b * x. Let's say, you want to predict who will win a chess game basing on the moves they make, you would use a tree-like (e.g.: alpha-beta pruning) algorithm to predict it.
* Linear relation: It is simply the relations where those relations can be explained by the y = a + b * x formula or even y = a + b1* x1 + b2*x2 + .... The simplest example is predicting the cost that is spent in the bar (or any kind of entertainment venue). cost = intercept (let's imagine you pay money for entering to the bar) + (the price of a drink) * (the number of drinks bought) + (the price of appetizer) * (the number of appetizers bought) would be our formula. 716