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What is the equation that shows the relationship among certain quantities?
The answer depends on the quantities and the nature of the relationship. It can be a line-of-best-fit (or regression line), or a formula.
Is the best fit line the same as the line of best fit?
Yes but phrased differently
What characteristic makes regression line of best fit?
The equation of the regression line is calculated so as to minimise the sum of the squares of the vertical distances between the observations and the line. The regression line represents the relationship between the variables if (and only if) that relationship is linear. The equation of this line ensures that the overall discrepancy between the actual observations and the predictions from the regression are minimised and, in that respect, the line is the best that can be fitted to the data set. Other criteria for measuring the overall discrepancy will result in different lines of best fit.
What is a line that is not a line but is almost a line?
A line of best-fit.
Why does best fit line does not touch all data points?
Because the "best fit" line is usually required to be a straight line, but the data points are not all on one straight line. (If they were, then the best-fit line would be a real no-brainer.)
