Workshop 23

Workshop 23 - CHEN 3010 Applied Data Analysis Fall 2004...

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CHEN 3010 Applied Data Analysis Fall 2004 Names: __________________________ __________________________ Workshop #23 Polynomial Linear Regression Objective Algebraic polynomial models are the most common used to represent engineering and scientific phenomena. In addition to fitting a polynomial model to the data, other issues need to be addressed: ¾ confidence intervals on the model parameters ¾ confidence interval on a prediction made by the fitted model ¾ analysis of residuals to determine model adequacy ¾ selection among different orders of polynomial In this workshop, you will deal with the first of these and learn how to fit polynomial models with Excel via two methods: ¾ vector/matrix calculations using Excel’s array operations ¾ the Analysis Toolbox (Data Analysis) Regression feature. Procedure 1. Log onto one of the lab plaza computers and download the Workshop23.xls file from the course web site. Launch Excel and open this workbook file. Enter your names for those present at the top of the worksheet to the right of the title. 2. Select all the composition values (%) and name this range Pct . Select all the heat capacity values and name this range y . Create an X-Y (Scatter) chart of the data on a separate chart sheet, displaying only markers. Add your group number to the title of the chart. 3. You will now carry out the regression calculations for a 4 th -order polynomial using Excel’s array operations. The formula to be implemented is ˆ β = [] ⋅⋅ XX Xy TT 1 First, enter labels in cells F5 through J5, as shown below: Then, enter the following in cells F6 through J6 :
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CHEN 3010 Workshop #23 Page 2 F6: 1 G6: =A6 H6: =A6^2 I6: =A6^3 J6: =A6^4 Select F6:J6 and drag-copy (fill handle) down through and including row 43. Double- check or correct if necessay that first column is filled with 1’s. You have created the X matrix for a 4 th -order polynomial. Select F6:J43 and name this range X .
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This note was uploaded on 10/11/2011 for the course CHEN 3010 taught by Professor Kompala,dh during the Spring '08 term at Colorado.

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Workshop 23 - CHEN 3010 Applied Data Analysis Fall 2004...

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