Maximum error expected as a percentage of full scale
Let your transfer function be \$y(x)\$ and approximated line be \$\overline{y(x)}\$. Then error \$\mathcal{E}\$ is,
 $$\mathcal{E(x)}= y(x) -\overline{y(x)} $$

The maximum value of error happens at \$x_0\$. ie, \$\mathcal{E_{max}} = \mathcal{E(x_0)}\$ . Where \$x_0\$ is given as,
$$\frac{d\mathcal{E}}{dx}|_{x=x_0} = 0$$

Now, maximum error expected as a percentage of full scale:
$$\frac{\mathcal{E_{max}}}{y_{max}-y_{min}}\times 100$$