The data set that shows a nonlinear association is the third set.
Which data set shows a nonlinear association?
The easiest way to check this is to graph the sets on an x-y plane, and see which of these graphs does not behave like a line.
But let's do another thing.
For each of the sets identify the increase in the independent variable, x, and then the increase in the y-variable.
For example, in the first table, we have the pairs:
(2, 3), (3, 4), (4, 5), etc...
This is clearly a linear relation of the form:
y = x + 1
So, writing each set in increasing order of the elements allows us to identify if it is linear or not.
Now let's go to the third option, the elements in order are:
(2, 2), (5, 4), (8, 10), ....
Notice that between the first two pairs, x increases by 3 and y increases by 2.
Between the second two pairs, x increases by 3 again, but y increases by 6.
Thus, this is not a linear relation.
We conclude that the correct option is the third set.
If you want to learn more about data sets:
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