First one question, which extent of reaction did you reach? If the conversion ratio is "low" (below 70%....) you probably will not be able to support your decision qua reaction order with solid statistics, and should acquire more data with higher conversion rates. On the othe rhand with low conversion ratio any order will give you acceptable predictions, so that may be sufficient for you. Chose the 0th order as it is simplest...

Is your reaction known? Then read what has been published.

Then do not look at the slope, look at the SHAPE and the associated fit: LOOK at the data and try the common linearizations (if 0 order you get a straight line in C= f(t) with parallel lines for different C0, if first order, the semi log is supposed to be linear, and C/C0  plots superimposable, is second order the 1/C is supposed to be linear).

Then go back to the raw data and fit it using the NON LINEARIZED equations, preferably using a software which will also give you the confidence plot; plot also the residuals ((measured - preducted) / measured)), if you have the right reaction order they should be randomly distributed.

Dr. Catherine, Thank you for your kind reply. I have attached a sample  file consisting of plot for zero-first-second order reactions of a compound. The initial concentration of the compound was 3900mg/L before staring the experiment. I 

You will have to plot your concentration versus time on semi-log paper and use the Arrhenius equation to determine the order of the reaction.

Use at least 6 points!

Semi log is applied only for first order reactions. Should I plot all three order of reaction on semi log sheet