For a direct linear relationship, the ratio between the
values of each variable should always be the same. Well, for a direct square
relationship, the ratio between the value of one variable and the square* *of
the other variable should always be the same. So say we had this table of
data:

x Sponsored Links |
2 |
3 |
4 |

y |
8 |
18 |
32 |

We could check whether a linear relationship existed by
finding the _{} or
_{} ratio
for each pair of values:

x |
2 |
3 |
4 |

y |
8 |
18 |
32 |

y/x |
4 |
6 |
8 |

These ratios aren’t the same, so it’s not a linear
relationship (so _{} *does not* describe this
data). We can check whether _{} describes the data by finding the
ratios of y/x^{2}:

x |
2 |
3 |
4 |

y |
8 |
18 |
32 |

y/x |
2 |
2 |
2 |

Bingo! The ratios are all the same. This means that y
is proportional to the square of x. Note that you could also have checked the *inverse*
ratios – so instead of checking y/x^{2}, we could have checked x^{2}/y.
The actual value of the ratio would have been different to ‘2’, but they would
still all be the same:

x |
2 |
3 |
4 |

y |
8 |
18 |
32 |

x |
0.5 |
0.5 |
0.5 |