I'm partly guessing exactly what you did, but I suggest it is because the method finds the line that minimises the sum square of errors, and when a smooth function is at a maximum or minimum the slope (derivative) of the function is zero.Amany Gouda said:Hello Sir,
I would studying the theory of least square and I find that the derivative of the error summation between the predicated line points and the true data is equal zero. Why the first derivative is equal zero?
A proof of which fact? That at an extremum the derivative is zero?Amany Gouda said:You are right, I have the same opinion regarding the answer. But is there a prove to this fact?
What does this mean? Did you find a proof but were unable to follow the logic of it?Amany Gouda said:Unfortunately, there is a prove but I didn't reach to it.
The least square method is a mathematical technique used to find the best fit line for a set of data points. It minimizes the sum of the squared differences between the actual data points and the predicted values from the line of best fit.
The least square method is commonly used in regression analysis to determine the relationship between two variables. It is also used in various fields such as economics, physics, and engineering to estimate unknown parameters from a set of data.
The least square method works by finding the line of best fit that minimizes the sum of the squared differences between the actual data points and the predicted values. This is done by calculating the slope and intercept of the line using the formula: y = mx + b, where m is the slope and b is the intercept. The values of m and b are then adjusted until the sum of the squared differences is minimized.
The least square method assumes that the data points are normally distributed, and that the relationship between the variables is linear. It also assumes that there are no significant outliers in the data and that the errors are independent and have equal variance.
The least square method is a simple and effective way to find the best fit line for a set of data points. It also provides a measure of how well the line fits the data through the calculation of the residual sum of squares. Additionally, the least square method is widely used and well understood, making it a reliable tool for data analysis.