Question

joseph claims that a scatterplot in which the y - values increase as the x - values increase must have a linear association. amy claims that the scatterplot could have a nonlinear association. which statement about their claims is true? joseph is correct because only a line will increase along the whole data set. the scatterplot will have a positive, linear association. joseph is correct because only a line will decrease along the whole data set. the scatterplot will have a negative, linear association. amy is correct because a nonlinear association could increase along the whole data set, while being steeper in some parts than others. the scatterplot could be linear or nonlinear. amy is correct because only a nonlinear association could increase along the whole data set. a line has the same slope at any point, but a curve can get steeper at different points.

Explanation:

A nonlinear association can also show an increasing trend (where \(y\) - values increase as \(x\) - values increase). For example, a quadratic function \(y = x^{2}+1\) (for \(x\geq0\)) is a nonlinear relationship where \(y\) increases as \(x\) increases. A linear association has a constant rate of change (constant slope), while a nonlinear association can have a non - constant rate of change (e.g., steeper in some parts than others). So, just because \(y\) increases as \(x\) increases does not mean the association is linear.

Answer:

Amy is correct because a nonlinear association could increase along the whole data set, while being steeper in some parts than others. The scatterplot could be linear or nonlinear.