LabQuest App curve fit coefficients are computed in one of two ways.

*** Linear form ***
Linear: y = mx +b

LabQuest App uses the same approach as Logger Pro. See:
How do you calculate linear fits in Logger Pro?

*** Non-linear forms ***
Proportional: y = Ax
Quadratic: y = Ax^2+Bx+C
Power: y = Ax^B
Natural Exponent: y = Aexp(-Cx)+B
Gaussian: y = A*e^(-(x-B)^2/(2*C^2))+D
Sine: y = A*sin(B*x+C)+D
Cosine: y = A*cos(B*x+C)+D
Cosine Squared: y = A*(cos(B*x+C))^2+D
Natural Logarithm: y = A*ln(B*x)

The coefficients of the non-linear forms are computed using the iterative, best-fit values approach of the Levenburg-Marquadt method. See–Marquardt_algorithm

The root mean square error (RMSE) and uncertainties for each coefficient are also computed.