**Tutorials on
Engineering Computations using Microsoft Excel**

The
following was found to be useful in teaching freshman engineering students to
use Excel for computations, particularly for data analysis. There are many textbooks and online tutorials
available (e.g., Google “Excel engineering data tutorial”). See also Help
in Excel itself. The tutorials below
were originally written for Excel 2003 and earlier versions. Most have been updated to Excel 2007 or 2010,
with the main difference between these is that for Excel 2010 being that the
File button is used to access options rather than the Office button in the
upper left corner. Starting with Office
2007, the new default file extension for Excel is xlsx,
which is
explained by Microsoft. For unknown
reasons, files created in this format on one computer have sometimes not been readable
on other computers. Therefore, it is
recommended that you save all Office files without the added x, i.e. as doc, ppt, or xls, especially if they
need to be opened on another computer.

**Performance of Excel 2007
on statistics computations **

**Improvements
and additions to Excel functions in Excel 2010** (Performance on test data not yet
reported in December 2010)

**Gnumeric Free open-source software
recommended by statisticians for those who want accuracy in statistical
computations using a spreadsheet.**
Graphing is more suitable for scientific and engineering plots than is
Excel. Additional features include
normalcy (normality) test and warning when inclusion of a variable in
regression analysis is not supported by the data.

**Performance of Excel and
Gnumeric on test data **(as
of June 2004)

**Useful
information:**

·
See
**format
conversions **for the relationships between formats in mathematics,
MATLAB and Excel.

·
**How to enter Greek letters, symbols, superscripts and
subscripts into Excel** ** **

·
**Common conversion
factors for units**

·
To
add arrows, text, etc. to a spreadsheet or graph, click on Insert,
Shapes. (This also works in Word and PowerPoint.)

·
To
add an equation, click on Insert, Object, Microsoft
Equation 3.0. (This also works in Word and PowerPoint.)** **The
resulting equation can be moved, enlarged and copied elsewhere.

·
Here’s
how to copy material from one file or web page into another file in Windows. Use one of the methods below to place the desired
material on the clipboard. Place the cursor where you wish the copied material
to be displayed. Then Paste Special. Double-click on it to bring up the
Format menu. Wrap Text, Square is
recommended to allow you to move the figure to wherever you want and resize it. To place something on the clipboard, use one
of the following procedures:

o For any portion of whatever’s on the
screen, use the Snipping Tool.

o For the window your cursor is on, press
Alt & Print Screen simultaneously.

o
For
everything on the screen, press the Print Screen button.

**Exercises:**

·
**Exercise 1**. Rudiments of Excel spreadsheets; entering names,
numbers and formulas into cells; editing, deleting and copying cell contents;
relative and fixed (absolute) cell references; built-in Excel functions; display
of equations in the spreadsheet; saving and formatting for printing.

·
**Exercise 2**. This exercise utilizes the Antoine equation with
constants for the vapor pressures of benzene and toluene to calculate the
composition of a vapor at one atmosphere pressure from a given liquid
composition, assuming ideal liquid and vapor mixtures in equilibrium. A
vapor-liquid phase diagram is generated thereby. Topics covered include
entry of formulas, copying these formulas, using Goal Seek to determine the
temperature required for a total pressure of one atmosphere, sorting, graph
creation, and formatting of spreadsheets and graphs. Goal Seek is located at Data / What-If Analysis. It is used frequently in engineering
calculations.

The
following exercises are all given in Excel files. Since Excel operations
may not available in your browser, it is recommended that you save the file to
your computer. This can be done by right-clicking on the link and then
Save Target. Then open it from the saved file using Excel. Several
of the exercises require tools that are not included in the default
installation of Excel. To install, find the add-in directions by clicking on the help icon (?
inside circle), search Add-ins, Load or unload add-in programs. Load the Analysis ToolPak
and Solver Add-in as indicated below. The Data Analysis and Solver icons
will then show up at the right end of the Data toolbar.

·
__Excel
2010 for Windows__: Click on File, Options, Manage Excel Add-Ins,
Go, Analysis ToolPak, OK.

·
__Excel
2007 for Windows__: Click on the Office Button in the upper left
corner, Excel Options, Add-Ins, Manage Excel Add-Ins, Go, Analysis ToolPak and Solver Add-in, OK.

·
__Excel
2008 for the Mac__: does not support
Visual Basic and so does not have these Add-ins will not run macros written
in previous versions of Excel.

·
__Excel
2011 for the Mac__: Reports indicate Visual Basic has again been
included, but not the Analysis TookPak. Apparently, Microsoft recommends the StatPlus:mac plug-in

·
**Exercise 3**. Use of the "if"
function to display the proper solution to the quadratic equation depending on
the values of the three constants.

·
**Exercise 4.
**In this exercise, a
data set is given, simulating measurements made of a single parameter.
The exercise is to characterize these data using the Descriptive Analysis and
Histogram tools contained within the Data Analysis package (Analysis ToolPak Add-In). Calculated will be the mean, median,
range, standard deviation, variance, kurtosis, skewness,
95% confidence limits, and the frequency and cumulative histogram.

**Definitions and equations for statistics**- See the extensive
**list of on-line materials**in statistics, including textbooks, graphical illustrations, and glossaries defining terminology. **Exercise 4a**. Creation of a so-called normal probability plot using Excel rather than probability paper. Used to provide another visual method of judging the normality of data.**MATLAB programs**for calculating descriptive statistics and details on their definitions.

·
**Exercise 5**. In the first part of this
exercise, a function is plotted and then approximated by a fifth order
polynomial using the Trendline correlating function on the resulting
graph. It is shown that this polynomial fits the function only within the
range utilized by Trendline. This illustrates one of the major problems
in using polynomials to correlate data. The other major problem is that
such correlations rarely reveal anything about the physics behind the
phenomenon. It is always better to fit data to a relationship with a
theoretical basis, whenever possible. If this isn't possible, one should
seek the simplest possible relationship, as this will be more likely to provide
clues to the physics involved. Polynomials should be the last resort.
In the second part of this exercise, another function is plotted in order to
obtain rough estimates of its three roots (x values giving y = 0). More
accurate values for the roots then are found by using the Goal Seek tool,** **which is at Data / What-If Analysis in Excel
2007 and 2010.

** Correlation of Data**:
By "correlation,"
we mean here an equation with constants that best fit the data. (It is
also possible to have a graphical correlation, but we do not consider that
here.) When the error in the values of the dependent variable is normally
distributed, "best" means the smallest sum of the squares of the
differences between the experimental values and those predicted by the
correlating equation. (These differences are called “residuals.”)
This is equivalent to maximizing the absolute value of the correlation
coefficient R, where R

When data vary over a wide range, you
may instead wish to minimize the relative error, i.e. the difference between
experimental and predicted values divided by the experimental value. This
is done by minimizing the sum of the squares of the differences in __logarithms__
of the experimental values and predicted values. When possible, it is
useful to repeat experiments so that you can determine whether the standard
deviation is approximately constant over the entire range of experimental
values, or whether the relative error is more constant. If the relative
error is more constant, then use logarithms. Depending on the equation
being fit, this may not be possible with the elementary tools in Excel, but
rather require the method shown in Exercise 11.

The following exercises deal with
examples of several correlating methods. For one dependent variable (y) and one
independent variable (x) that obey one of five simple equations, the simplest
method is to use the Trendline function on a graph. If this is not
possible, you must first linearize the equation and calculate the new
variables. The Regression tool can be used for multiple linear regression
analysis if more than two such variables emerge from this linearization.
If linearization is not possible, you can use the Solver Add-In to find the
coefficients in the equation that minimize the sum of the squares of the residuals.
This is known as non-linear regression analysis. Since more than one
minimum sometimes exists, the solution obtained may depend on the initial
assumptions made for these coefficients.

·
**Exercise 6**. Data are given for the
resistance/length of a wire (H) versus its cross-sectional area (A).
These data are correlated first by plotting the data and using the Trendline
function on the resulting graph. Then they are correlated by finding the
average value of HA. Other correlation methods are possible; some are
given in the solution to this exercise.

·
**Exercise 7**. Three sets of x-y data and
three correlating equations are given. You are asked to determine which
equation best fits which set of data. This is done by plotting the data
using linearized forms of the equations and then using Trendline for a linear
equation. The best fit can readily be seen by comparing the resulting
line with the data points, as well as by the highest value of R^{2}.

·
**Exercise 8**. The Solver Add-In tool is used
to find the minimum in a function of two variables, and the diameter of a
cylinder giving the minimum in its surface area for a specified volume.

·
**Exercise 9**. Data are given for a parameter
measured by two different techniques for several different conditions.
You are asked to make as many conclusions as possible. Possible
techniques include plotting versus condition number; using the Descriptive
Statistics tool in the Data Analysis package on the measurements using
individual techniques and on the differences in their values; and the t-Test
tools.

·
**Exercise 10**. Data are given for the vapor
pressure of CO versus temperature. You are asked to use the Antoine
equation to correlate these data, i.e. to find the constants in the Antoine
equation giving the best fit. A linearized form of the Antoine equation
is given that has three new variables, not two. These three variables are
calculated in columns adjacent to one another. The Regression tool is
used to find constants for the linearized form, from which the Antoine equation
constants are calculated. (The Regression tool requires the independent
variables, x1, x2, etc., to be in adjacent columns. This tool performs
what is known as multiple linear regression analysis, which, basically, is least-squares for more than one independent
variable. Matrix methods are utilized by Excel for the calculations.)

·
**Exercise 11**. This is a continuation of
Exercise 10. The same data are now correlated by using the Solver Add-In
to maximize R^{2}, which is equivalent to minimizing the sum of the
squares of the deviations between the logarithms of the experimental vapor
pressures and the predicted values. Since the Antoine equation is not
linearized in this exercise, this process constitutes non-linear regression analysis.
As noted above, the values of the constants found by Solver may depend on the
initial assumptions. Such behavior is common for
minimization/maximization algorithms. It is as if you are blindfolded,
placed somewhere in the Adirondack mountains, and then
asked to find the highest mountain. Unable to see, you can only sense
whether you are going uphill or downhill. By continually progressing
uphill, you will eventually find the nearest mountain -- but not the highest
among all mountains. That is, if there are many maxima your algorithm
will find one of them, but the one it finds will depend on where you start and
may not be the very highest. In other words, it may find only the local extremum rather than the global extremum.
Engineers dealing with optimization problems seek to find algorithms that
overcome this difficulty. Sometimes the
first use of Solver gives only an approximate result, so run it again to make
certain. More advanced optimization
tools are included in Excel 2010, but these will not be addressed here. Solver support and tutorial

·
**Exercise 12.
**This exercise
considers the special case of fitting an equation with 0 intercept. While
Excel finds the correct constants for the equation, its results for SS, MS, F
and significance F seem strange and, it turns out, are controversial.** **Rather
than the customary definitions and computation methods described at **Interpretation,
**for the Total SS Excel now calculates the sum of the squares of the
experimental values of the dependent variable, rather than the sum of the
squares of the __differences__ between these values and their average.
The Residual SS is calculated in the usual way, but the Regression SS is the
new Total SS minus the Residual SS. Apparently, this was done to avoid a
negative Regression SS, which occurs when a correct fit would pass nowhere near
the origin. This, however, gives a meaningless value for F and its
significance. But why would one try to fit data with a 0 intercept when
this would obviously be inappropriate? This is demonstrated in some
detail in this exercise, along with what is believed to be the correct approach
and a reasonable alternative. Draw you own conclusions.

Created by **Professor William R. Wilcox **at
Clarkson University.
Please email him your comments and suggestions. Additional examples and
exercises are sought. * *

*Last
revised June 13, 2012.*

·
**Chemical engineering
design information**

·
**MATLAB:
tutorial on symbolic methods for calculus, graphing, and solution of equationsl **

·
**MATLAB: tutorials
on analysis and plotting of data **

·
**MATLAB: tutorial
on numerical solution of equations **

·
**On-line information on
statistics and design of experiments**

·
**Clarkson's Department of
Chemical and Biomolecular Engineering**