Y intercept

Expand the three detemiinants D, Dt, and for the least squares fit to a linear function not passing through the origin so as to obtain explicit algebraic expressions for b and m, the y-intercept and the slope of the best straight line representing the experimental data. 

Starting with equation 5.6, show that the equations for the slope, y-intercept, and x-intercept in Figure 5.7(a) are correct. 

The most commonly used form of linear regression is based on three assumptions (1) that any difference between the experimental data and the calculated regression line is due to indeterminate errors affecting the values of y, (2) that these indeterminate errors are normally distributed, and (3) that the indeterminate errors in y do not depend on the value of x. Because we assume that indeterminate errors are the same for all standards, each standard contributes equally in estimating the slope and y-intercept. For this reason the result is considered an unweighted linear regression. 

Finding the Estimated Slope andy-Intercept The derivation of equations for calculating the estimated slope and y-intercept can be found in standard statistical texts and is not developed here. The resulting equation for the slope is given as... 

These standard deviations can be used to establish confidence intervals for the true slope and the true y-intercept... 

Calculate the 95% confidence intervals for the slope and y-intercept determined in Example 5.10. 

Equations 5.13 for the slope, h, and 5.14 for the y-intercept, ho, assume that indeterminate errors equally affect each value of y. When this assumption is false, as shown in Figure 5.11b, the variance associated with each value of y must be included when estimating [3o and [3i. In this case the predicted slope and intercept are... 

An appropriate standard additions calibration curve based on equation 5.8 plots Sspi elVo + Vs) on they-axis and CsVs on the x-axis. Clearly explain why you cannot plot Sspike on the y-axis and Cs[ Vs/( Vo Vj)] on the x-axis. Derive equations for the slope and y-intercept, and explain how the amount of analyte in a sample can be determined from the calibration curve. 

A plot of AEi/2 versus log [F], therefore, gives a straight line. The slope of the line is used to determine the stoichiometric coefficient, p, and the y-intercept gives the value for the formation constant [3. ... 

Eor a pseudo-zero-order reaction a plot of [A]( versus time should be linear with a slope of -k, and a y-intercept of [A]o (equation 13.8). A plot of the kinetic data is shown in figure 13.7. Linear regression gives an equation of... 

A plot of 1/v versus 1/[S], which is called a double reciprocal, or Lineweaver-Burk plot, is a straight line with a slope of Km/Vmax) a y-intercept of 1/Vmax> and an x-intercept of-l/Km (Figure 13.11). 

Plotting measured versus accepted gives fexp = 0.679 for the y-intercept and fexp = 0.345 for the slope. Because f(0.05, 3) is 3.18, there is no evidence for a significant difference between the values. 

Application of IP and NCS in conjunction with specification tolerance limits enables to substantiate acceptance criteria for linear regression metrological characteristics (residual standard deviation, correlation coefficient, y-intercept), accuracy and repeatability. Acceptance criteria for impurity influence (in spectrophotometric assay), solution stability and intermediate precision are substantiated as well. 

Write the Lineweaver-Burk (double-reciprocal) equivalent of this equation, and from it calculate algebraic expressions for (a) the slope (b) the y-intercepts and (c) the horizontal and vertical coor-... 

Mols of component, i, at start of distillation Total mols of liquid in bottoms of still at time, Tj Total mols liquid (not including any steam) in bottom of still at start time Tq (batch charge) y intercept of operating line or constant at fixed pressure for Winn s relative volatility Mols of component, i, in bottoms No. components present, phase rule or no. components, or constant... 

Intercepts are points where the curve of a function crosses the axes. The x intercepts are found by setting y = 0 and the y intercepts by setting x = 0. 

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