Cyclic voltametry. Simulation and analysis of reaction by Gosser D.K.

By Gosser D.K.

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P, are the estimates of the parameters. The values of βj that minimize SS(Res) are obtained by setting the derivative of SS(Res) with respect to each βj in turn equal to zero. This gives (p + 1) normal equations that must be solved simultaneously to obtain the least squares estimates of the (p + 1) parameters. It is apparent that the problem is becoming increasingly difficult as the number of independent variables increases. The algebraic notation becomes particularly cumbersome. For these reasons, matrix notation and matrix algebra are used to develop the regression results for the more complicated models.

An equivalent test of the null hypothesis that β0 = 0 can be made using the difference between the residual sums of squares from the intercept and no-intercept models. This test is discussed in Chapter 4. 8 Models with Several Independent Variables Most models will use more than one independent variable to explain the behavior of the dependent variable. The linear additive model can be extended to include any number of independent variables: Yi = β0 + β1 Xi1 + β2 Xi2 + β3 Xi3 + · · · + βp Xip + i .

A boldface capital letter is used to designate a data vector and a boldface Greek letter is used for vectors of parameters. Thus, for example,   3 8 v =   is a 4 × 1 column vector. 2 1 µ = ( µ1 µ2 µ3 ) is a 1 × 3 row vector. We usually define the vectors as column vectors but they need not be. 1, or 0 is called a scalar. A square matrix has an equal number of rows and columns. D = 2 6 4 7 Vector Square Matrix is a 2 × 2 square matrix. A diagonal matrix is a square matrix in which all elements are zero except the elements on the main diagonal, the diagonal of elements, a11 , a22 , .

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