Course Name: Financial Time Series Analysis for Trading, Section No: 6, Unit No: 5, Unit type: Quiz
In this Question, why is Cubic relation not Linear..Cubic is Linear, coz it stays constant(Linear)
Hi Surender,
Usually, a linear relationship between two variables is one where the graph of the relationship is a straight line. The general form of a linear equation is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept. Linear relationships have a constant rate of change.
On the other hand, a cubic relationship is a type of polynomial relationship of degree 3. The general form of a cubic equation is y = ax^3 + bx^2 + cx + d, where x is the variable, and a, b, c, and d are constants.
The key difference is in the shape of the graph. A cubic function does not produce a straight line; instead, its graph takes the form of a curve. The cubic function's graph may have one or more turning points, and the rate of change is not constant throughout the domain.
To clarify, a cubic relationship is not considered linear because its graph does not follow a straight line; it exhibits a more complex curve. Linear relationships, in contrast, have a constant rate of change and produce a straight-line graph.
Hope this helps.
Thanks, but not clear…
what do u think is y=b+2x^3
is that linear? Is that cubic?
In this case, whatever number u put in for independant variable x, it will be steep straight regression line, not curvilinear line…
please correct if i am missing something
The equation y = b+2x^3 is a cubic equation, not a linear one. In a linear equation, the highest power of the variable (in this case, x) is 1. The general form of a linear equation is y = mx + b where m is the slope and b is the y-intercept.
In contrast, your equation y = b+2x^3 has the highest power of x as 3, making it a cubic equation. Cubic equations describe curves with a single, pronounced bend, unlike linear equations that represent straight lines.
The term 2x^3 in your equation contributes to the cubic behavior. If you were to plot this equation on a graph, you would observe a curve with more complex behavior than a simple straight line.