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The least square regression line of x to y is a mathematical function, right?
Not quite right. Least square regression is a statistical analysis method, which is used to estimate the linear relationship between two variables in a set of data. The least square method determines this relationship by solving a straight line, so that the sum of squares of the distances from the sample point to the straight line is the smallest.

So the least squares regression line itself is not a mathematical function, but a linear equation in the form of y = a+bx (where a and b are constants).

Of course, in some cases, this regression line can be regarded as a function. For example, in the case of simple linear regression (that is, there is only one independent variable), the regression line can be regarded as a functional relationship between input X and output Y. However, on the whole, it is more like a statistical model than a mathematical function.