Regression Lines: Why Pass Through Mean for Accuracy?

[Cheman]

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. :-)

 

[Zurtex]

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.

 

[tacman]

A regression line, also known as a line of best fit, is a straight line that represents the relationship between two variables. It is used to predict the value of one variable based on the value of another variable. The accuracy of the regression line is crucial in making reliable predictions.

According to statisticians, the regression line should pass through the mean of x and mean of y because it minimizes the sum of squared residuals. Residuals are the differences between the actual values and the predicted values on the regression line. By passing through the mean of x and mean of y, the regression line ensures that the sum of squared residuals is minimized, making it the best possible fit for the data.

Moreover, the regression line passing through the mean of x and mean of y also ensures that the line is unbiased. This means that on average, the predicted values on the regression line will be equal to the actual values. This is important because an unbiased regression line is more accurate in predicting values for new data points.

In summary, the regression line passing through the mean of x and mean of y is important because it minimizes the sum of squared residuals and ensures an unbiased prediction. This makes the regression line more accurate in predicting values for new data points, thus making it a crucial tool in statistical analysis.