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If you plot data points on a graph the rarely will form a straight line. Least squares is a method of finding a line 'close' to all the data points instead of just guessing and drawing a line that looks good.
If you have a line, then there is an algebraic formula to find the distance from each point to that line. Then using statistics, you can make the statistically averaged distance from each data point as close as possible to a line. The distances are squared, averaged, and the average of those squared distances may be used to find the regression line.
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What negative correlation indicate?
the negative sign on correlation just means that the slope of the Least Squares Regression Line is negative.
What is the line that most clearly fits a set of data called in math?
A regression line.
Can you obtain R-square from standardized regression model?
yes
What is another name for line of best fit?
linear regression
If the regression sum of squares is large relative to the error sum of squares is the regression equation useful for making predictions?
If the regression sum of squares is the explained sum of squares. That is, the sum of squares generated by the regression line. Then you would want the regression sum of squares to be as big as possible since, then the regression line would explain the dispersion of the data well. Alternatively, use the R^2 ratio, which is the ratio of the explained sum of squares to the total sum of squares. (which ranges from 0 to 1) and hence a large number (0.9) would be preferred to (0.2).
