Stating your hypotheses clearly and using a 5% level of significance, test whether or not there is evidence of a negative correlation between the age of a van and its resale value.

The manager decides to test a non-linear model. She codes the data using $m={\log }_{10}x$ and $n={\log }_{10}y$ and finds the regression line to be $n=1.35-0.48m$.

The product moment correlation coefficient between $m$ and $n$ is calculated as -0.94.

Explain how this value supports the use of a non-linear model.

Show that the relationship between $x$ and $y$ can be expressed in the form $y=a{x}^b$, where $a$ and $b$ are constants to be determined.