Through two points

Once factor values are determined, the minimum number of experiments is governed by the number of coefficients in the model, but if only the minimum number of experiments is done, there is no way to check the model. An analogy is drawing a straight line through two points, which cannot fail, but measurement of a third point will allow a least squares lit with some indication of the status of the linear model. 

When you plot values of a variable z on a logarithmic axis and your plot yields a straight line through two points with coordinate values zi and zz, replace zz - Z with In (c2/ Ci) ( = In Z2 - In zi) in the formula for the slope. 

Just as a straight line touching a curve, may be regarded as a line drawn through two points of the curve infinitely close to each other (definition of tangent), so a circle in contact with a... 

Drawing a line through two points under measurement... 

If we keep two terms in the RHS of Eq. 7.78, the resulting formula is equivalent to a linear equation passing through two points (t , y ) and (t i y i). Similarly, if three terms are retained, the resulting formula corresponds to a parabolic curve passing through three data points (t ,y ), U -i, y -i) and (t 2, y -2)- Note that these latter points are prior to (t , y ). 

When lines are defined in the contexts of points, lines, and circles, the situations outlined in Figure 7-6 are the most frequent. A line may be at a distance from a line or at an angle with a line. Sometimes it goes through two points. A hand sketch approximates a shape intended by an engineer it is processed into the specified or best-fit analytic curve. A line can be tangent to a... 

Insert pH electrodes and titrate potentiometrically with 0.1 M ethan-olic potassium hydroxide through two points of inflection. 

Titrate the effluent from the cation-exchange column potentiometrically with ethanolic 0.1 M sodium hydroxide through two points of inflection at pHs below and above 7. 

It is possible to draw a straight line through two points. The general equation of a straight line through two points Pj and P2 ( 2/ 2) can be... 

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