What does the Standard Error of Estimate measure?

What does the Standard Error of Estimate measure?

• A. It gives a measure of the standard distance between the predicted Y values on the regression line and the actual Y values in the data.
• B. It measures the spread of the X values.
• C. It represents the standard deviation of Y.
• D. It indicates the precision of the correlation coefficient.

Answer: (A)

Standard Error of Estimate tells you how far, on average, the actual Y values are from the values predicted by the regression line. It is the standard deviation of the residuals, where a residual is the difference between the observed Y and the predicted ŷ. A smaller SEE means the regression line predicts Y more accurately; a larger SEE indicates more variability in how far the actual data fall from the line. It isn’t about how spread out the X values are, nor is it the same as the standard deviation of Y itself. It also doesn’t measure how precise the correlation coefficient is. In simple regression, SEE is the square root of the sum of squared residuals divided by n−2, reflecting the typical prediction error around the line.

Standard Error of Estimate tells you how far, on average, the actual Y values are from the values predicted by the regression line. It is the standard deviation of the residuals, where a residual is the difference between the observed Y and the predicted ŷ. A smaller SEE means the regression line predicts Y more accurately; a larger SEE indicates more variability in how far the actual data fall from the line. It isn’t about how spread out the X values are, nor is it the same as the standard deviation of Y itself. It also doesn’t measure how precise the correlation coefficient is. In simple regression, SEE is the square root of the sum of squared residuals divided by n−2, reflecting the typical prediction error around the line.