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As far as I know, all of the variables except c can be determined mathematically. My question is this, using calculus or any other method, is there a way to determine c without graphing the data?

As a follow up, is there a general formula or procedure that applies to all types of Regression (linear, Cubic, Sinusoidal, etc.)? I want to know this because I believe it is possible using statistical concepts like variance and I want to find out how many of these can be done completely by hand without graphing.