In observations of equal precision, the most probable values of the observed quantities are those that render the sum of the squares of the residual errors a minimum, is the fundamental principle of A. Gauss’ Mid Latitude formula B. D’Alembert’s method C. Legendre’s method D. Least square method

The correct answer is D. Least square method.

The least squares method is a standard approach to estimating the parameters of a statistical model. It minimizes the sum of the squares of the residuals, which are the differences between the observed values and the values predicted by the model. The least squares method is often used in regression analysis, where the goal is to find a linear relationship between two or more variables.

Gauss’ Mid Latitude formula is a formula used to calculate the latitude of a point on the Earth’s surface. It is based on the assumption that the Earth is a sphere.

D’Alembert’s method is a method for solving systems of linear equations. It is based on the principle of superposition, which states that the solution to a system of linear equations can be found by adding the solutions to the individual equations.

Legendre’s method is a method for approximating functions. It is based on the idea of using polynomials to approximate the function.

In observations of equal precision, the most probable values of the observed quantities are those that render the sum of the squares of the residual errors a minimum. This is the fundamental principle of the least squares method.