The following formula was used in the estimation of a physical constant:
Assuming that x10 = 10, x20 = 40, X30 = 7, and X40 = 70, calculate y. Estimate the approximate standard deviation of y given that the standard deviations of the x's are σ1 = 5, σ2 = 7, σ3 = 4, σ4 = 10. Obtain the necessary derivative (a) algebraically and (b) numerically. Using the numerical method, check the linearity assumptions.