I have seen this question languish for a couple of days with no answer, so I thought I might try to help. My expertise is in statistics and within solar, in PV output, however, I thought I might start the ball rolling.

From a statistics viewpoint, I need to know something about the model you are interesting in fitting with regression. You mention a, c, k, and n, so perhaps it is a model based upon those variables. If so, what functional form on a,c ,k, and n do you posit for that model. If that can be specified, and there are data for these variables, then a model can be fit. If the model is linear in respect to the coefficients of those variables (many types of non-linearity in respect to the variables can be accommodated, e.g, a polynomial model) then an ordinary least-squares multiple regression might be used, although it would depend on data and theory whether such a model is the best choice. Else, other fitting algorithms could be used.

Because you have a ratio as your response variable, you should be open to the possible need to re-express your data. One possibility with ratios is to take them in the other order--that is, to use a reciprocal re-expression. You also appear to have a time series, so you will want to account for autocorrelation. Another alternative is to model the changes in the moisture ratio over time. I agree with John that you need to say more about your data and your goals. But first, you need to plot your data to see what you have. Is it very noisy (bouncing around a lot) or does it show a pretty smooth curve?

Dear John Morris thank you for your answer. Yes i have all the experimental data available but i don't know how to fit that data using multiple regression to estimate these variables (a, c, k and n).

Dear Paul F Velleman thank you for your answer.The curve drawn based upon experimental data isn't smooth but polynomial. All the experimental data available but i don't know how to fit that data using multiple regression to estimate these variables (a, c, k and n).