Check Your Confidence: Size Really Does Matter

Heather A. Carlson describes the influence of many factors on linear regression and highlights the limits that they impose. A simple least-squares linear regression starts with a fit line that must intersect the point, the average calculated and experimental values. The fit is then dictated by finding a slope that minimizes the squared distances in the y direction between the data points and the fit line. A tighter correlation means better agreement between the data points and the fit line; therefore, there are smaller residuals and a tighter distribution of those residuals around the value zero. A tighter distribution means that there is a smaller standard deviation of the distribution of the residuals for the data points and a higher R. Experimental error can be incorporated as error bars in the y direction if there is a need to address some difference in uncertainty between different data points. This simply calls for a weighted linear regression.