The following formula is the SCS equation for evaluating Cumulative Infiltration :
$$z=at^b+c$$ In the equation $c=0.6985$ is a constant but I am allowed to use $c=0.7$ as an estimation. I have a table for the values of $z$ and $t$ ( it denotes the cumulative infiltration for the any specific time $t$ and I evaluated $z-c$ too) :
$$\begin{array}{|c|c|} \hline t& z&z-c \\ \hline 5&1.7&1 \\ \hline 10& 2.7&2\\ \hline 15& 3.6&2.9\\ \hline 25& 5.1 &4.4\\ \hline 45& 6.2&5.5\\ \hline 60& 7.7&7\\ \hline 75& 9.2&8.5\\ \hline 90& 10.7&10\\ \hline 110& 12.7&12\\ \hline 130& 14.7&14\\ \hline \end{array}$$
Then we have $z-c=at^b$ and I substitute $z-c=z'$ and then by taking logarithm we have:
$$\ln(z')=\ln(a)+b\ln(t)$$
Then in order to find the value of coefficients $a$ and $b$ I choose two points $t_1=10 , z'_1=2$ and $t_2=15 , z'_2=2.9$ and evaluated their logarithms and after substituting in the above equation I got system of equations and found $\ln(a)$ and $b$ and finally $a$ and $b$.
But in the second part of the question I am asked to evaluate the accuracy of these three coefficients for the estimation of $z$. I have no idea how to do it. Am I supposed to taking differentiate or something like that?