Final answer:
Statistical regression, or regression towards the mean, refers to the phenomenon where extreme observations are followed by more moderate ones. An example is a basketball player scoring very high in one game and then closer to their average in the next. In terms of linear regression, it is about finding a line of best fit for data points and understanding outliers relative to that line.
Step-by-step explanation:
Statistical regression, often known as regression towards the mean, is a concept in statistics that describes how extreme observations are followed by more moderate ones over time. It's commonly observed in situations where there is natural variability and the same measurement is taken repeatedly.
For an original example, imagine a basketball player who has an exceptional game and scores 30 points, well above their average. The ‘regression towards the mean’ concept would suggest that in the next game, it's likely that the player will score closer to their average, say 15 points, simply due to statistical fluctuation and the natural variability of their performance.
Using the regression equation can also refer to finding a line of best fit through a set of data points. In the context of the SAT scores and GPA relationship from the question, the median-median line approach would be a way to define such a line. Remember that all points won't perfectly align with the regression line due to the inherent scatter of real-world data.
To identify potential outliers, you could look at points in a scatter plot that are more than two standard deviations from the regression line. These outliers could disproportionately affect the line's slope and correlation coefficient. Removing an outlier may result in a line that better fits the remaining data, as reflected by a lower sum of the squared errors (SSE).