Rockwell Automation 9307 FactoryTalk EnergyMetrix - Manual (Page 199)

8 • ChartsPlus
199
Regression Analysis
ChartsPlus displays the standard regression line as a black line on the X-Y trend chart.
The regression line (known as the least squares line) is a plot of the expected value of the
dependent variable for all values of the independent variable. The regression line is the
one that best fits the data on a scatter plot. A linear regression on X-Y chart is calculated
by using the least squares method.
The regression coefficients correspond to the formula:
y = (m1 * x1) + b
The coefficient m1 represents the slope of the regression line, and b represents the Y-
intercept, which is the value of Y when X1 is zero.
The correlation coefficient R expresses the strength of the linear relationship between X
and Y. The values of correlation coefficient range from -1 to 1. The closer the correlation
coefficient to 0, the weaker the relationship between regression variables. For example,
-0.9 describes strong negative correlation, 0.9 describes strong positive correlation, and
0.2 describes weak positive correlation.
Multi-variable Regression
You can specify up to 3 independent X variables. Since a multi-variable plot cannot be
displayed in 2 dimensions, a separate chart tab will appear for each selected X variable,
each showing the relationship between the selected Xn and Y variables. The Targeting tab
displays the regression coefficients in the Standard X1, Standard X2 and Standard X3
rows. The coefficients correspond to the formula:
y = (m1 * x1) + (m2 * x2) + (m3 * x3) + b
Excluded Points
You can exclude points by double-clicking them with the mouse. Excluded points appear
as a red X on the chart. When a point is excluded, the standard regression line is
recalculated. To restore a single excluded point, double-click it once more. To restore all
excluded points, click the Reset button on the Targeting tab.
Targeting
Targeting compares the data set to a user-selected target line, which appears as a red line
on the X-Y chart. You can select among four types of targets:
 Conservative - drops all data points above the standard line to the standard line
 Aggressive - discards all data points above the standard line
 Use all data - target line = standard line
 Manual - you can select and enter coefficients into data entry fields and click the
Update button
To clear the target line select the Chart Setup tab and click the Plot button. The target line
will not appear if more than one independent (Xn) variable is selected.