I just worked with ELISA this morning, and some of my samples result show concentration of IL-6 is less than minimum (from std curve). Does this make sense? thanks

Very little information to comment on.
Normal human serum from healthy people contains less then 10ng/l IL-6 so it's very likely that if you're testing human serum there are samples below the lowest standardvalue.

Is possible that results are < 0 or lowest standard.
But, did your controls work properly?
If you ran duplicates (samples or standards/calibrators)was the CV acceptable?

Always a chance...slight chance of heterophile abs.
If you can run samples again diluted 1:2 or 1:10 and you get positive result then you have heterophile ab. Other option is run samples by different method/kit mfg.

sorry i am not very familiar about the statistical work, and how do i check my coefficient of variation whether is acceptable or not?

btw, is it acceptable that i draw my linear regression as 0,0 intercept? i modified my graph by 0,0 intercept, and now the IL-6 concentration has positive value. does this make sense?

how bt if i use plasma for IL-6 detection, will there be any significant difference with serum samples?

Thanks