Regression Lines: Why Pass Through Mean for Accuracy?

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SUMMARY

A regression line, or line of best fit, must pass through the means of the x and y variables (x̄ and ȳ) to ensure accuracy in predictions. This requirement stems from the least squares method, which minimizes the sum of the squared differences between observed values and the regression line. By intersecting at the means, the regression line effectively balances the data points, leading to a more reliable representation of the relationship between the variables.

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Cheman
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Why according to statisticians should a regression line (line of best fit) pass through the mean of x and mean of y? (ie - x bar and y bar) Why does this make the regression line more accurate? Thanks in advance. :-)
 
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The line of best fit is the line that best fits the average of the points right? This would mean the point where it is the exact average of x and the exact average of y would be quite an obvious point on this line.
 

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