Intercept spreadsheet calculation

A double logarithmic plot, given in Fig. 19.20(b), allows determination of the oxidation parameters k and n. A change in the oxidation mechanism (e.g. spallation or breakaway oxidation) becomes apparent by a change in the slope in the double logarithmic plot. Analysis of the linear part of the curve by linear regression using simple spreadsheet calculations yields the slope, b = 1/n, and the y-axis intercept, as shown in Fig. 19.20(b). The values for the oxidation parameter k and the exponent n as well as the number of... 

One difficulty with the Trendline is that the equation only appears graphically. The values for slope and intercept have to be copied manually into the spreadsheet if they are to be used in later calculations. 

The method of least squares is used to determine the equation of the best straight line through experimental data points. Equations 4-16 to 4-18 and 4-20 to 4-22 provide the least-squares slope and intercept and their standard deviations. Equation 4-27 estimates the uncertainty in x from a measured value of y with a calibration curve. A spreadsheet greatly simplifies least-squares calculations. 

Spreadsheet Summary In the first exercise in Chapter 10 of Applications of Microsoft Excel in Analytical Chemistry, a spreadsheet is developed to calculate the electrode potentials as a function of the ratio of reductant-to-oxidant concentration ([R]/[0]) for the case of two soluble species. Plots of E versus [R]/[0] and E versus log([R]/[0]) are made, and the slopes and intercepts are determined. The spreadsheet is modified for metal/metal ion systems. 

Once it has been verified that the data can be properly fit to a one-compartment bolus IV model, a linear regression analysis is performed on the data, with time (t) entered as the independent (x) data, and In(Cp entered as the dependent (y) data. Linear regression analysis can be performed on calculators that handle two-variable statistics, or using spreadsheet, graphing, or statistical analysis software on a computer. The analysis should provide values for the intercept (b) and the slope (m) that provide the best possible fit to the measured data in the form y = b + mx, as illustrated in Figure 10.23. The linear regression analysis also often provides a value called the correlation coefficient (r). 

We can use the Excel statistical functions to calculate the slope and intercept for a series of data, and the R value, without a plot. Open a new spreadsheet and enter the calibration data from Example 3.21, as in Figure 3.9, in cells A3 B7. In cell A9 type Intercept, in cell A10, Slope, and in cell All, R Highlight cell B9, click on / Statistical, and scroll down to INTERCEPT under Function name, and click OK. For Known x s, enter the array A3 A7, and for Known y s, enter B3 B7. Click... 

The LINEST program of Excel allows us to quickly obtain several statistical functions for a set of data, in particular, the slope and its standard deviation, the intercept and its standard deviation, the coefficient of determination, and the standard error of the estimate, besides others we will not discuss now. Linest will automatically calculate a total of 10 functions in 2 columns of the spreadsheet. 

The linear least-squares line gives a slope of 0.861 and an intercept of —0.002 (using Options under Chart, Add Trendline, when highlighting the chart or line). Hence, the concentration of the unknown is equal to (0.463 — 0.002)70.861, as given by the formula in the spreadsheet (below). The sample concentration is 0.540 ppm. We will now perform the same calculation without charting the calibration curve, and including the standard deviation of the sample concentration. 

Zero the instrument with distilled water and aspirate the diluted unknown and the standard addition samples. The absorbance increases in the latter are due to the added calcium. Using a spreadsheet, prepare a plot of absorbance against added concentration of calcium (starting at zero added, i.e., the sample). From the jc-axis intercept of the plot, determine the concentration of calcium in the diluted unknown. See the spreadsheet in Chapter 17 for preparation of a standard additions plot and unknown calculation. Calculate the concentration in the original sample. How does this method account for phosphate interference ... 

The spreadsheet and Stern-Votmer plot are shown in Figure 15-4. The data are entered into columns B and C, and F /ris calculated in column D. The slope and its standard deviation are - 210 0.9 M" as obtained from the spreadsheet statistics. Note that the intercept is very nearly unity. 

The uncertainty of the slope and intercept values can be calculated by standard statistical techniques. These calculations are straightforward in an EXCEL spreadsheet. An example is provided in Appendix 6-C. In fact, the calculations can be done automatically with the Data Analysis package in EXCEL. 

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