Final answer:
The phrase 'standard deviation of residuals' is the correct term for the average distance that observed values fall from the regression line in regression analysis, where it indicates the typical scatter of data points around the line of best fit.
Step-by-step explanation:
The standard deviation of the residuals is the average distance that the observed values fall from the regression line. In regression analysis, residuals are the differences between the observed values of the dependent variable (y) and the predicted values () that are calculated using the line of best fit. The standard deviation of these residuals can be calculated to determine the typical distance that the data points deviate from the regression line, giving us an idea of the scatter around the line of best fit.
This is particularly useful for identifying outliers, which are observed values that fall far from the regression line. Typically, an outlier is any data point that is more than two standard deviations away from the predicted value on the least squares regression line. Detecting these outliers could indicate exceptional cases or errors in data collection.
Understanding the coefficient of determination (²), which is the square of the correlation coefficient (r), also enlightens the analysis. A coefficient of determination of 0.44, for example, tells us that approximately 44 percent of the variation in y can be explained by the variation in x using the regression line, with the remaining 56 percent being unexplained by x, illustrating the dispersion of points around the fitted line.