By Peter Englezos

A reference and textbook supplying readers with crucial optimization equipment for parameter estimation in chemical engineering. The CD-ROM positive factors Fortran desktop courses for fixing equation structures and different issues of Microsoft Excel and Sigma Plot. includes over 900 equations in all.

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Example text

Set the logical value Comt=true if you wish to calculate a y intercept value. Step 7. Step 8. Set the logical value Stats=true if you wish the program to return additional regression statistics. Step 9. Now that you have entered all the data you do not hit the OK button but instead press Control-Shift-Enter. This command allows all the elements in the array to be displayed. If you hit OK you will only see one element in the array. Once the above steps have been followed, the program returns the following information on the worksheet.

19b become I. 28a) Z«f I"? N and x. 28b) Chapter 3 32 The parameters estimates are now obtained from N 1- -] k2 k3 >4. 6 5 N 4 3 N V x / ; i Yx Zj i Y x Zw i i=l i=l i=l i=l i=l N N N N N x 5i N 4 V / jx \ N IX i=l N x 3 V / -jx i N 2 Y / -j x i N N Z»f*i N N Z«? Z^r Z«i i=l i=l i=I Z ? 29) ZX^i i=l N §y' STATISTICAL INFERENCES Once we have estimated the unknown parameter values in a linear regression model and the underlying assumptions appear to be reasonable, we can proceed and make statistical inferences about the parameter estimates and the response variables.

N+\) unknown parameters, y i ; = k , x n i + k 2 x, 2i +... y 2 ; = k, x 2 ii + k2x22i +... 5a) y mi ~ ky x m [, + k 2 x n]2 j +. 6) It should be noted that the above definition of Xj is different from the one often found in linear regression books. There X is defined for the simple or multiple linear regression model and it contains all the measurements. In our case, index i explicitly denotes the ith measurement and we do not group our measurements. Matrix Xj represents the values of the independent variables from the i* experiment.

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