Y-error

Figure 2.9. The confidence interval for an individual result CI( 3 ) and that of the regression line s CLj A are compared (schematic, left). The information can be combined as per Eq. (2.25), which yields curves B (and S, not shown). In the right panel curves A and B are depicted relative to the linear regression line. If e > 0 or d > 0, the probability of the point belonging to the population of the calibration measurements is smaller than alpha cf. Section 1.5.5. The distance e is the difference between a measurement y (error bars indicate 95% CL) and the appropriate tolerance limit B this is easy to calculate because the error is calculated using the calibration data set. The distance d is used for the same purpose, but the calculation is more difficult because both a CL(regression line) A and an estimate for the CL( y) have to be provided.

The correlation coefficient ranges between -1 and +1. An error correlation of+1 indicates that the errors in both x and y for any particular measurement of an x, y pair will always be in the same direction (either both greater than, or both less than the true values). An error correlation of -1 indicates that the x error will always be in the opposite direction than the y error. An error correlation of zero indicates that the x- andy -errors are independent of one another. 

Figure 1. Results of Monte Carlo simulations for 1500 pairs of x, y points with a mean of 100, Ganssian errors of 10 (1 o), and four different x-y error correlations (p). Elhpses show 95% confidence hmits for the joint x-y distribution. Note that the ellipses extend farther than the 2o range of either the x or j errors themselves—a non-intuitive characteristic of joint distributions that arises because an x- (or y-) value deviating less than expected permits ay- (orx-) value that deviates more than expected.

Using error crosses as isochron data-point symbols where significant x-y error correlations exist ... 

Within each of the two classes in Table V, the first two sets of limits ((a), (b), (d), (e)) use the constant and variable weights, respectively, and assume B and A are exactly known (model-1 in Table IV). The remaining limits involve estimated parameters, based on the design x and the equations of Table III. Method (c) utilizes the parameters of Model-1 and constant weight method (f) uses Model-3 and variable y-errors (weight). 

IP Set up a spreadsheet to reproduce Figure 4-13. Add error bars Double click on a data point on the graph and select Y Error Bars. Check Custom and enter the value of sy in each box for the + and — error. Better yet, enter the cell containing sy in both boxes. 

Perhaps the most common situation involving graphing scientific data is to generate a linear regression plot with y error bars. In most situations, the error in the x data is regarded as being so much smaller than that of the y data that it can... 

Figure 2. Effect of errors in x, T, Zi5 and Z2 on the calculated standard deviation of the y-error in Equation 11 (1) 4 simultaneous errors (2) x-error (3) 7T-error (4) Zrerror (5) Zg-error...

Figure 11.6 Summary of single particle fluorescence vs. SPR peak position measurements by Chen et al. with three different fluorescent dyes. The SPR peak positions are binned in 20 nm intervals along the x-axis. The average fluorescence intensity observed from particles within each bin is then plotted as a fimction of the SPR position for silver nanoprisms functionalized with (A) Alexa Fluor 488, (B) Alexa Fluor 532, and (C) Rhodamine Red dyes. The excitation spectra (dotted lines) and emission spectra (dashed lines) are plotted for reference for each dye. The solid line is a guide to the eye. Y-error bars represent the standard deviation of the mean fluorescence intensity observed from particles with SPR peaks within each 20 nm bin. D) Schematic illustrating use of DNA oligonucleotides to conjugate fluorophores a finite distance from the nanoprism surface. Reprinted with permission from reference [25] (2007)...

Each Ci = y, — y, error term is a random variable that is assumed independent of all the other values. However, when the error terms are self- or autocorrelated, the error term is not but e, i + That is, e,- (error of the ith value) is composed of the previous error term e, i and a new value called a disturbance, do The di value is the independent error term with a mean of 0 and a variance of 1. 

To add error bars, click on one of the points to highlight all points on the graph. In Chart Tools, Layout, select Error Bars and choose More Error Bars Options. For Error Amount, choose Custom and Specify Value. For both Positive Error Value and Negative Error Value, enter D4 D9. You just told the spreadsheet to use 95% confidence intervals for error bars. When you click OK, the graph has both jc and y error bars. Click on any jc error bar and press Delete to remove all jc error bars. 

The ordinary linear least-squares regression is based on the assumption of an independent and normal error distribution with uniform variance (homoscedastic). In addition, linear regression based on ordinary least-squares presumes that errors in signal are much higher than those in concentration [error (Y) error (X)] it is also very sensitive to extreme data points, which may result in biased values of the regression parameters, slope, and intercept. 

Input var. Y, dep. var Norm.X Norm. Y Pred.Norm.Y Pred. Y Error AAD ARD... 

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