Question

Looking at a plot, why is it clear that a regression line exists? That is, why is it clear that the error ?(?,?) has a global minimum?

This is a general question. Not for a specific plot.

Answer 1

Regression analysis ia a statistical techniques that attempts to explore and model the relationship between two or more variables . In regression line one variable is dependent variable and another is independent variable. For regression wh have need minimum two variable ,one is dependent and another is independent. When we Plot a diagram between two variable then we saw that any relationship between them is exist, whether it is linear or curvilinear. When linear regression line between variable that is in plot we see a straight line graph and curviilinear when graph between variable is not straight line. From plotting graph or scatter diagram , we must see a or we clear that a regression line exist.

Now from regression line we calculate the coefficient of regression line which measure what percent of independent variable variable explained dependent variable. We minimize tha distance between observed or experimental value to predicted line or predicted regression line .

The above method caleed least square method that makes the vertical distance from the data points to the regression line as small as possible. It's called a "Least square " because the best line of fit is one that minimize the variance (The sum of square of the variance).

Thus error has global minimum.