Regression Data for Final Project G3 Stat 615.MPJUsin.docx

Regression Data for Final Project G3 Stat 615.MPJ
Using Minitab for Statistical Analysis
Davenport University
Statistics Courses
Created by
David Poock
Deb Steiner
Updated by
John Suttkus
Preface
This document only provides basic information on using
fundamental commands in Minitab to analyze data. Any
interpretation of results is the responsibility of the instructor.
The included sample output is only used to demonstrate the
typical results.
We are thankful for the work of Nicholas Scheal, an adjunct
instructor at Davenport University, in creating the first version

of this guide.
Table of Contents
General Minitab Information 5
Downloading a Copy of Minitab from the Davenport Library
Website 5
Starting Minitab on a Davenport computer 5
Session and Worksheet Windows 5
Entering Data into a Minitab Worksheet 6
Saving Minitab worksheets/projects: 7
Copying and Pasting into a Word Processor: 8
Editing a Graph in a Word Processor: 8
Creating Tables 9
Frequency Tables - Individual Values 9
Frequency Tables – Using class intervals 10
Creating Graphs 12
Histogram 12
Frequency Polygon 14
Ogive 15
Dotplot 15
Stemplot 17
Bar Chart (or Bar Graph) 18
Pareto Chart 19
Pie Chart 20
Scatterplot 21
Time-Series Graph 21
Boxplot 22
Calculating Descriptive Statistics 24
Correlation & Regression Analysis 26
Correlation Coefficient and P-Value 26
Regression Equation and R-squared 26

Fitted Line Plot 28
Probability Distributions 29
Binomial Probability Distribution 29
Poisson Probability Distribution 30
Uniform Probability Distribution 30
Normal Probability Distribution 31
Confidence Intervals 33
Confidence interval: population mean, μ 33
Confidence interval: population proportion, p 34
Hypothesis Testing 35
Hypothesis Testing: population mean, μ 35
Hypothesis Testing: population proportion, p 36
Minitab Guide Fall 2011 – Updated Spring 2015 1
General Minitab InformationDownloading a Copy of Minitab
from the Davenport Library Website
On your home computer or laptop, click here, or log in to your
Davenport STUDENT CONNECTION webpage. Scroll down to
STUDENT TOOLS and click on the Library link. Under , click
on MiniTab and then download Minitab for either a PC or a
MAC. If you have trouble installing Minitab on your home
computer, please call IT at 1-877-899-1499.Starting Minitab on
a Davenport computer
If you are on a Davenport computer, type Minitab in the Search
Windows box at the bottom of the desktop screen and then
select Minitab.

MiniTab is a statistical software package designed for easy
interactive use. For a quick introduction to Minitab, go to
http://www.minitab.com/en-us/support/documentation/ and click
on Getting Started with Minitab 17.Session and Worksheet
Windows
After opening Minitab, you will see a display of its two main
windows: the Session window at the top and the Worksheet
window at the bottom. The Project window is minimized below
the Worksheet window. Only one window will be active at any
time. You can make a window active by clicking in it or
choosing it from the Window menu.
Window menu.
This is the minimized Project window.
This is the Worksheet window.
This is the Session window.
The Session window displays calculated results in text format.
Text in this window can be formatted, copied and pasted into
another document, or deleted.
The Worksheet window consists of a spreadsheet for entering
data in columns. Minitab allows you to have multiple
worksheets open at one time. When you have more than one
worksheet in a project, the active worksheet is indicated by
three asterisks (***) following the worksheet name in the title
bar. If multiple worksheets are open, commands will act only
upon the data in the active worksheet. You can make a
particular worksheet active by clicking in it or choosing it from
the Window menu. You can also toggle between the worksheets
by hitting CTRL D.Entering Data into a Minitab Worksheet
In Minitab, there are three types of data: (1) numeric data
(numbers), (2) text data (characters), and (3) date/time data.

The data columns are identified as C1, C2, C3, etc.
Immediately under these column labels, you will find an empty
gray cell to enter the column title (above row 1 of the data set).
This is where you can label each column with a name that
represents the data stored in that column. Many of the
operations that we will be performing are done by referring to
specific columns, so to help, Minitab lets you give the columns
a name so you know what is in it. For example, if you have
variables that are pulse rates, then you can call that column
“Pulse.”
It is wise to enter a meaningful name for the different columns
of data so it becomes easy to keep track of what’s stored in each
column in the dataset.
The three asterisks indicate that this is the active worksheet.
Type in the column names here.
Entry of sample data is very simple. Click on the first cell
of the desired column, type a number, then press the Enter key.
Then type a second number and press the Enter key again.
Continue this process until all of the sample data have been
entered. If you make a mistake, simply click on the wrong
entry, type in the correct value, and hit Enter.
Note, the direction of the arrow in the upper left corner of
the worksheet tells you the entry direction when you are
entering data. (We call this arrow the data entry direction
arrow.)
To enter data column wise, click the data entry direction arrow
to make it point down. After you type a value and press Enter,
the active cell moves down.
To enter data row wise, click the data entry direction arrow to
make it point to the right. After you type a value and press

Enter, the active cell moves to the right.
Although Minitab worksheets have rows and columns into
which you can type values and generate commands, it does not
work exactly like a spreadsheet in Excel. The functionality of
the worksheets in Minitab is generally defined by columns
rather than by individual cells. For example, a single column
can contain only one type of data (text, numeric, or date/time).
In addition, if you want to assign a formula in the worksheet so
that calculated values can be updated automatically when data
are added or changed, you must assign the formula to an entire
column, not to individual cells.
Tip: To zoom in or out to increase or decrease the size and
number of cells displayed in the worksheet, press the CTRL key
while scrolling your mouse wheel when the worksheet is active.
Many times data can be copied and pasted directly into Minitab
from a spreadsheet, document, or website. Make sure you
double check that the data has been copied into the correct
columns in Minitab. You may have to adjust the spaces
between data values before coping and pasting so the data is
pasted into the correct column.Saving Minitab
worksheets/projects:
After entering your data, you can save the dataset as a
Minitab worksheet as follows:
1. Click on File.
2. Click on Save Current Worksheet As …
3. A dialog box will then be displayed. In the “Save in” box,
enter the location where you want the worksheet saved. In the
“File name” box, enter the name of the file. You can omit the
extension of .MTW; it will automatically be provided by
Minitab.
4. Click on Save.
The above commands will only save the active Minitab
worksheet. If you have multiple worksheets open and/or have

done some calculations and created some graphs, you will want
to save all of this together in a Minitab Project. You can save
your project as follows:
1. Click on File.
2. Click on Save Project As …
3. A dialog box will then be displayed. In the “Save in” box,
enter the location where you want the project saved. In the
“File name” box, enter the name of the project. You can omit
the extension of .MPJ; it will automatically be provided by
Minitab.
4. Click on Save.
Again, saving the Minitab project saves all output in the session
window, any graphs that were created, and any alterations made
to the worksheet(s). When you reopen the project, you can
resume working where you left off.
Copying and Pasting into a Word Processor:
To copy a stem-and-leaf plot, descriptive stats, regression
analysis results, a confidence interval, or results of a hypothesis
test from the session window into a word processor, copy and
paste as usual. Click and drag to highlight what you want to
copy. Click on “Edit” and choose “Copy.” Alternatively, after
highlighting, right-click and choose Copy, or hit CTRL C. Then
go to the word processor and choose “Paste.” Alternatively,
right click and choose Paste, or hit CTRL V.
To copy a graph into a word processor, click on the graph then
click “Edit” and choose “Copy graph.” Then go to the word
processor and choose “Paste.” The same alternative methods
work here. Make sure you clicked on the graph first. Then
either right click and choose Copy, or hit CTRL C. (If you
don’t click on the graph, it will copy something from the
session window or worksheet instead of the graph.) Once in the
word processor, either right click and choose “Paste,” or hit

CTRL V.
You can resize the graph by (single) clicking on the graph and
dragging any of the corners towards the center of the graph.
ONLY use the corners, as this will preserve the ratio.Editing a
Graph in a Word Processor:
When a graph has been copied into a word processor, it can still
be edited. Double click on the graph. It takes a few seconds,
but you will see slash marks (////) appear all around the graph
(see below). While the slash marks are around the graph, your
word processor is actually transferring your work to Minitab.
You are able to alter colors, fonts, and other aspects of the
graph just as if you were in Minitab creating the graph. To
finish, click away from the graph outside of the slash marks.
This returns the graph to your word processor and the slash
marks go away.
Creating Tables
Many of the examples in this manual make use of the female
pulse rate data in the FHEALTH.MTW worksheet provided in
the STAT 220 textbook, Elementary Statistics (11th Edition) by
Mario F. Triola. (Data Set 1, Appendix B, page 767, Column
5).
For your convenience, the dataset has also been provided below:
Frequency Tables - Individual Values
To create a frequency table of individual values, do the
following:
1. Enter or retrieve the data into a Minitab column.
2. Click Stat. Choose Tables and then choose Tally Individual
Variables.
3. Enter the variables you want to make a frequency table for in
the Variables box. Immediately below is the option for Counts
(frequencies), Percents (relative frequencies), Cumulative
Counts (cumulative frequencies), and Cumulative Percents

(cumulative relative frequencies). The nice thing about Minitab
is that you can create all the frequency tables in a single step.
Choose any of the options that you want to use by checking
each one’s box. (If you know you are going to look at all four,
you can check all four and only have to make one table.)
4. Click OK.
These tables will be displayed in the Session window.
Using the female pulse rate data (column C5) in the
FHEALTH.MTW worksheet, the following results were
obtained:
Tally for Discrete Variables: PULSE
PULSE Count Percent CumCnt CumPct
60 3 7.50 3 7.50
64 4 10.00 7 17.50
68 5 12.50 12 30.00
72 8 20.00 20 50.00
76 6 15.00 26 65.00
80 6 15.00 32 80.00
88 5 12.50 37 92.50
96 1 2.50 38 95.00
104 1 2.50 39 97.50
124 1 2.50 40 100.00
N= 40
Here, the frequency table gives the number of times each
individual value appeared. If we wanted to create a frequency
table with class intervals, we could now use the tally counts
found above to see how many data values fall into each class.
For example, we would see that there are 12 data values falling
into the class of 60 – 69 (3 at 60, 4 at 64, and 5 at 68, for a
total of 12).

Another way to obtain a frequency distribution with data
separated into classes is to generate a stemplot (described later
in this handout, page 16). The frequency counts for the classes
can be found by simply counting the number of digits to the
right of each stem.
There is also a third method that we can use in Minitab to create
a frequency distribution with the data separated into classes.
The steps are given next.Frequency Tables – Using class
intervals
To create a frequency table using class intervals, do the
following:
1. Enter or retrieve the data into a Minitab column.
2. Click Data. Choose Code and then choose Numeric to Text.
This willchange the individual values into the values of the
classes that you want for your frequency table.
3. In Code data from columns enter the column of the original
data, and enter a new column for Store coded data in columns
(this is where the output will go).
4. In Original values you need to specify each range of
numbers. For example, 60:69 is how you type in 60, 61, …, 69.
Then in the New box directly across from it, type in 60 - 69.
This replaces any values of 60, 61, …, 69 with the new label of
the class.
5. Repeat this for each of the classes (see below).
6. Click OK.
To create the frequency table with classes, create the frequency
table as before (Stat – Tables –Tally Individual Variables) using
the new data in the stored column. The difference is that now
instead of using the original data you use the new column of
coded data (that shows the classes).

Note, the table generated by Minitab using this method doesn’t
always have the class intervals in numerical order. For
example, Minitab created the frequency and relative frequency
tables below for the female pulse data. As you can see, the
classes are not listed in order, which will cause the cumulative
frequencies and cumulative percents to be inaccurate.
Therefore, it is suggested that this method only be used for
“counts” and “percents”, and not for cumulative totals. Instead,
after rearranging the classes from lowest to highest, the
cumulative totals can be found by hand.
C2 Count Percent
100 - 109 1 2.50
120 - 129 1 2.50
60 - 69 12 30.00
70 - 79 14 35.00
80 - 89 11 27.50
90 - 99 1 2.50
N= 40
(Note also that if a class has a frequency of 0, it will not show
up in the table.)
Creating Graphs
Most of the graphs we will create in Minitab can be found under
the Graph menu item. We will create the following graphs:
Histogram, Relative Frequency Histogram, Frequency Polygon,
Ogive, Bar Chart, Dotplot, Stem-and-leaf Plot, Pie Chart,
Scatterplot, Time-series Plot, and Boxplot. (We will also
create a Pareto Chart, but this is found under the Stat menu
item.)
Histogram
A histogram can be used to explore the distribution of a
quantitative data set. It examines the shape and spread of
sample data. A histogram is constructed by drawing bars

(rectangles) for each class of data (either using midpoints or
class boundaries (cutpoints) ). The height of each bar is the
frequency of the class.
Below is the Minitab procedure for generating a Histogram:
1. Enter the data in a Minitab column, such as column C1. If
the data are already stored in a Minitab worksheet, retrieve the
worksheet.
2. Click on the main menu item Graph.
3. Select Histogram and click on the option of Simple. Then
click OK.
4. Place your cursor in the “Graph Variables” box and either
type in the column label that contains the data you want to use
(such as C1) or double click on the column in the left box.
5. If you want to give the histogram a title, click on Labels and
type the title in. You can also add grid lines by clicking Scale
and clicking the Gridlines tab (Use MAJOR ticks).
6. Click OK to display the Histogram.
Using Minitab, the following histogram for the female pulse
rates was created.
Here, the vertical axis represents the frequency. If you want to
make a relative frequency histogram (instead of the default
which is frequency) then before step 6 above, click on Scale and
select the Y-scale Type tab. For a relative frequency histogram,
choose the Percent button and then click OK.
If you want to change the look of the histogram, you can double
click on the attribute that you want to change. For example, if
you double click on the background, you can change its color. If
you double click on any of the titles, you can change the font,

size, orientation, etc. If you double click on the bars of the
histogram you can change the color, pattern, etc. (You can
change color under the first tab that says “Attributes”.)
Histograms created in Minitab divide sample values into
intervals called bins. Bins are intervals used to sort sample data
for graphing. In Minitab, histograms plot bars that represent
the number of values falling into each bin (its frequency).
Note: observations that fall exactly on an interval boundary are
included in the interval to the right (or left, if it is the last bin).
The number of bins influences the appearance of a graph. If
there are too few bins, the graph will be unrefined and represent
the data poorly. If there are too many bins, many of them will
be unoccupied and the graph may have too much detail. For
example, the histograms below represent the same data:
Minitab automatically calculates and uses an optimal number of
bins. The middle graph (15 bins) is the Minitab default for this
dataset. However, you can change the number of bins, as
desired. Bins can be defined by either their midpoints (center
values) or their cutpoints (class boundaries).
To change the binning of a histogram from midpoint to cutpoint
positions (which is how graphs usually look), do the following:
1. Double click anywhere on the X-scale of the histogram.
2. In the Edit Scale pop-up window, click on the Binning tab,
select Cutpoint under Interval Type, and then select
Midpoint/Cutpoint positions under Interval Definition.

3. You will have to type in the values of the cutpoints in the
following fashion: low end: high end / interval length. For
example, 10:50/5 starts the first bar (bin) at 10 – 15, the next
bar at 15 – 20, and so on up to the last bar of 45 – 50. Also,
0:4/0.5 would have bars (bins) of 0.0 – 0.5, 0.5 – 1.0, ..., 3.5 –
4.0.
4. Click OK.
To see the height (frequency) of a bar, hover your cursor over
it.Frequency Polygon
A frequency polygon is similar to a histogram, but instead of
plotting bars with heights corresponding to the frequencies, we
plot points at the midpoints of each class interval. The height
of a point corresponds to the frequency of that class. The
points are then connected with a line.
Here is the Minitab procedure for generating a frequency
polygon:
worksheet.
click OK.
5. Click on Data View. Under Data Display, uncheck “Bars”
and check Symbols (this makes the dots).
6. Click the Smoother tab. Click on Lowess, and change Degree
of smoothing to 0. (this connects the dots).
7. Click OK twice to display the frequency polygon.
The following frequency polygon was created for the female

pulse rates. (Note, the default binning was changed to midpoint
positions of 65, 75, 85, … 125 using the methods on the
previous page.)
Ogive
Here is the Minitab procedure for generating an ogive:
worksheet.
click OK.
5. Click on Scale and then on the Y-Scale Type tab. Check the
box for Accumulate values across bins.
6. Click on Data View. Under Data Display, uncheck “Bars”
and check Symbols.
7. Click the Smoother tab. Click on Lowess, and change Degree
of smoothing to 0.
8. Click OK twice to display the ogive.Dotplot
Dotplots are used to assess and compare distributions. A dot
plot is drawn by placing each value in the data set horizontally
in increasing order and placing a dot above the value each time
it occurs.
Here is the Minitab procedure for creating a dotplot.
worksheet.
2. Click on the main menu item of Graph.
3. Select Dotplot, then choose Simple, and click OK.

5. Click OK to display the dotplot.
Shown below is the Minitab dotplot display of the female pulse
rates. The original dotplot showed values on the horizontal
scale of 63, 72, 81, …, 117, but the dotplot was modified to
show the more convenient values of 60, 65, 70, …, 125 instead.
This change in the numbers used for the horizontal scale was
made by double-clicking on any number on the horizontal scale,
selecting the Scale tab, and then typing 60:125/5 in the box
labeled Position of ticks.
If possible, Minitab displays a dot for each observation.
Otherwise, a dot represents multiple observations with a
footnote indicating the maximum number of observations
represented by each dot.
Note, you can make several dotplots at one time by entering all
the columns of data to plot in the “Graph Variables” box.
Minitab displays a separate graph for each column. To panel all
graphs on the same page, click on the “Multiple Graphs” box
and choose Multiple Variables. Under “Show Graph Variables”,
select In separate panels on the same graph.
Note, the dotplots may have different scales. You can make it
so the dotplots have the same scale by clicking on Same x,
including same bins (see below.)
Stemplot
Minitab can provide stemplots (or stem-and-leaf plots). The
textbook notes that a stemplot represents data by separating
each value into two parts: the stem (such as the leftmost digit)
and the leaf (such as the rightmost digit).
Stemplots are used to examine the shape and spread of sample
data. Minitab displays a stem-and-leaf plot in the Session

window. The plot is similar to a histogram on its side, however,
instead of bars, digits from the actual data values indicate the
frequency of each bin (row).
One advantage of the stem-and-leaf plot over frequency
distributions and histograms is that the raw data can be
retrieved from the stem-and-leaf plot. (Once a frequency
distribution or histogram of data is created using classes, the
raw data are lost.)
Here is the Minitab procedure for generating a stemplot.
worksheet.
2. Click on the main menu item of Graph.
3. Select Stem-and-Leaf.
5. If you have a number of groups that you want to make
separate stem-and-leaf plots for but the numbers are all in one
column, you can use By Variable to separate the column. E.g.:
separate by car make, or freshman/sophomore/junior/senior,
either of which would be stored in another column.
6. Minitab automatically chooses whether or not to stretch the
stem-and-leaf plot. If you do not like the way the stem-and-leaf
turned out, you can set the “Increment” to the desired value
(such as 10). (You can just delete the one you already made
and create a new one).
7. Click OK.
Shown below is the Minitab stem-and-leaf plot that results from
the female pulse rates. (Again, these results will be displayed
in the Session window.)
Stem-and-leaf of PULSE N = 40

Leaf Unit = 1.0
7 6 0004444
12 6 88888
20 7 22222222
20 7 666666
14 8 000000
8 8 88888
3 9
3 9 6
2 10 4
1 10
1 11
1 11
1 12 4
The above stem-and-leaf plot is the default that is automatically
generated by Minitab. In this case, it is an expanded stemplot,
with classes of 60-64, 65-69, 70-74, 75-79, and so on.
To obtain a stem-and-leaf plot that is not expanded, enter an
Increment value of 10. The new results are shown below.
Stem-and-leaf of PULSE N = 40
Leaf Unit = 1.0
12 6 000444488888
(14) 7 22222222666666
14 8 00000088888
3 9 6
2 10 4
1 11
1 12 4
From the stem-and-leaf plot, you can see that the first five
values in the dataset are pulse rates (in beats per minute) of 60,
60, 60, 64, and 64. The maximum pulse rate in the dataset was
124.

The display has three columns:
· The leaves (right) – Each value in the leaf column represents a
digit from one observation. The "Leaf Unit" (declared above
the plot) specifies which digit is used. In this example, the Leaf
Unit is 1.0 so it represents a digit in the unit (or one’s) place
value.
· The stem (middle) – The stem value represents the digit
immediately to the left of the leaf digit. In the example, the
stem value of 6 indicates that the leaves in that row are from
observations with values greater than or equal to 60, but less
than 70; the stem value of 7 indicates values greater than or
equal to 70, but less than 80, and so on.
· Counts (left) – These values represent some cumulative counts
– you can ignore this column (it won’t be used).
Bar Chart (or Bar Graph)
(Using either frequencies or relative frequencies)
One of the most common devices for graphically representing
qualitative data is a bar chart. A bar chart is constructed by
labeling each category on the horizontal axis and the frequency
(or relative frequency) of the category on the vertical axis.
Bars of equal width are drawn for each category and the height
of each bar represents the category’s frequency (or relative
frequency).
Use the following steps to construct a bar chart from individual
data values (raw data).
worksheet.
2. Click on the main menu item Graph. Select Bar Chart.
3. In the “Bars represent” pull-down menu, select Counts of
unique values. Click on Simple. Then click OK.

4. In the “Categorical variables” box, click on the column with
the data so that the column label (such as C1) or the data name
appears in the box.
5. Click on Labels to add a title to the graph. You can add grid
lines by clicking Scale and clicking the Gridlines tab (use
MAJOR ticks).
6. Click OK to display the bar chart.
You can also have the height of each bar represent the relative
frequencies instead of the frequencies. Before step 6 above, in
the Bar Chart dialog box, click on Chart Options and select the
box Show Y as percent.
Use the following steps to construct a bar chart from a table of
values (summarized data).
1. Enter the categories (labels) in C1 and the frequencies or
(relative frequencies) in C2. If the data are already stored in a
Minitab worksheet, retrieve the worksheet.
2. Click on the main menu item Graph. Select Bar Chart.
3. In the “Bars represent” pull-down menu, select Values from a
table. Click on Simple. Then click OK.
4. In the Graph variables box, enter C2 (or the column that
contains the frequencies). In the Categorical variable box, enter
C1 (or the column that contains the categories you want to use
to make the bar chart).
5. Click on Labels to add a title to the graph. You can add grid
lines by clicking Scale and clicking the Gridlines tab (use
MAJOR ticks).
6. Click OK to display the bar chart.Pareto Chart
A Pareto chart is a bar graph for qualitative data, with the bars
arranged in decreasing order of frequency. The tallest bar is at
the left, and the smaller bars are farther to the right.
Here is the Minitab procedure for constructing a Pareto chart:
1. If you have raw data, enter it in column C1 (or any other
desired column). If you have summarized data in a table, enter

the categories (labels) in one column (such as C1) and the
frequencies in a separate column (such as C2).
2. Select the menu items of Stat, Quality Tools, and Pareto
Chart.
3. In the Defects or attribute data in: box, enter the column
that contains the categories
(labels). This is the only column you need to enter if you
have raw data. If the data is
summarized in a table, enter the frequency column in the
Frequencies in box.
4. Click Do not combine. If you don’t want the ogive
overlapped with the Pareto chart, click
on Options, and check the Do not chart cumulative percent
box.
5. Click OK to display the Pareto chart.
Pie Chart
A pie chart is a circle divided into sectors (or wedges). Each
sector represents a category of data. The area of each sector is
proportional to the frequency of the category.
Here is the procedure for using Minitab to construct a Pie chart
from individual data values (raw data).
1. Enter the raw data in column C1 (or any other desired
column).
2. Select the main menu item of Graph. Then select Pie Chart.
3. When the dialog box is displayed, select the Chart counts of
unique values option.Click in the “Categorical Variables” box.
Enter the column that contains the data you want to make a pie
chart for.
4. Under Pie chart options you can change the order of the
pieces from the order they appear in the data to increasing
volume (smallest to largest) or decreasing volume (largest to
smallest).
5. Click Labels and choose the Slice Labels tab. Here you can
choose to label the slices of the pie with their name and either

their frequency or percent (you typically would not do both
frequency and percent).
6. Click OK to display the pie chart.
To see the percent of each wedge, hover your cursor over it.
Here is the procedure for using Minitab to construct a Pie chart
from a table of values (summarizeddata).
1. Enter the table in a worksheet – labels in one column,
frequencies in another column.
2. Select the main menu item of Graph. Then select Pie Chart.
3. When the dialog box is displayed, select the Chart values
from a table option.Click in the “Categorical Variables” box.
Enter the column that contains the data you want to make a pie
chart for. Click in the “Summary Variables” box and enter the
column of the frequency values.
4. Pie Chart Options and Labels work the same as with Pie
Charts from individual data. (See steps 4 and 5 on the previous
page.)
5. Click OK to display the Pie chart.
Scatterplot
A scatterplot can be very helpful in identifying a relationship
between two variables. (In particular, we will be looking for
linear relationships in this class.)
Here is the Minitab procedure for generating a scatterplot.
1. Given a collection of paired data, enter the values for one of
the variables in a column (such as C1), and enter the
corresponding values for the second variable in another column
(such as C2). Be sure to enter the two columns of data so that
they are matched in the same way that they are paired in the
original listing.
2. Click on Graph from the main menu.

3. Select Scatterplot, Simple, then click OK.
4. Enter the variable you want on the left side (y-axis) under “Y
variables” and the one you want along the bottom (x-axis) under
“X variables”.
5. You can add grid lines by clicking Scale and clicking the
Gridlines tab (Use MAJOR ticks).
6. Click OK to display the scatterplot.
Another procedure for generating a scatterplot is to select Stat,
Regression, then Fitted Line Plot. We will use this option later
when we discuss the topics of correlation and regression (see
page 28). For now, we are simply generating the scatterplot to
visually explore whether there is an obvious pattern that might
reveal some relationship between the two variables.Time-Series
Graph
Time-series data are data that have been collected at different
points in time, and Minitab can graph such data so that
changing trends become easier to recognize.
Here is the Minitab procedure for generating a time-series
graph.
1. Given a collection of time-series data, enter the sequential
values in column C1
2. Select the main menu item of Graph. Select the menu item of
Time Series Plot,Simple, then click OK. (If you want to show
two things at once, you can choose Multiple instead).
3. A dialog box now appears. In the “Series” box you need to
put the variables you want to keep track of over time.
4. Click on “Time/Scale.” You need to choose the time scale
that you are using. Most of the time, you are looking at
Calendar and specifically choosing Year or possibly Day or
Month. Then you need to set the Start Values. Click “One set
for all variables” and fill in the starting date in the box (such as
1990). In the “Increment” box fill in the length of time between
data values (if you gathered every year, the increment is 1; if

you gathered every three years, the increment is 3, etc.). (See
next page.)
5. Click OK. Click on Labels. Click on the Data Labels tab.
Click Use y-value labels.
6. Click OK twice to display the time-series graph.
Boxplot
Here is the Minitab procedure for generating a boxplot.
worksheet.
3. Select Boxplot and click on the option of One YSimple.
Click OK.
type in the column label(s) that contain the data you want to use
(such as C1) or double click on the column(s) in the left box.
If you have a number of groups that you want to make separate
Boxplots for but the numbers are all in one column, instead of
“One Y Simple” click on One Y With Groups. Enter the column
with the numbers in the “Graph Variables” box and you can use
“Categorical Variable” to separate the column. E.g.: separate by
car make, or freshman/sophomore/junior/ senior, either of which
would be stored in another column.
5. Click on Scale and check the box Transpose value and
category scales. This will change the boxplot so it runs
horizontally instead of vertically (which is the Minitab default).
You can also add grid lines by clicking the Gridlines tab (Use
MAJOR ticks).
6. Click OK twice to display the boxplot.
Below is the boxplot for the female pulse rates. Note that
Minitab creates a modified boxplot. Any value that it calculates

to be an outlier is shown as an asterisk.
Calculating Descriptive Statistics
To display numerical statistics like the Mean, Median, Mode,
Standard Deviation, etc., do the following in Minitab:
1. Click Stat and choose Basic Statistics and then
DisplayDescriptive Statistics. You can display the descriptive
statistics of more than one variable one by one or all at once.
In the Variables box, list the column(s) that you want the
descriptive stats for.
2. If you have data that can be separated by classes but the data
is all in the same column (like information on GPAs can be
separated by classes of freshman, sophomore, etc.) and you
want to see the descriptive stats for each, then you enter the
variable that separates the classes in the By variables box. (For
the previous example, “c1ass” would go in this box.)
Otherwise, leave this box blank.
3. Click on Statistics. Here you can choose which descriptive
statistics you wish to display. Check / uncheck all boxes as
desired. For example, if we do not need SE of Mean, N
missing, or N non-missing, then you can uncheck these boxes.
Depending on what you are looking at you may wish to check
the boxes for Range, Interquartile range, Variance, Coefficient
of Variation, Skewness, or N Total.
4. Click OK twice to display the statistics.
The results will be displayed in the Session window.
Again, as mentioned in Step 1, you can enter more than one
variable and get all the statistics at once. When you are
entering the columns in the “Variables” box, enter as many as
you want. Under “Options” you can still choose the individual

statistics to report. When you hit OK, the Session window will
look as follows:
Descriptive Statistics: Data 1, Data 2
Total
Variable Count Mean SE Mean StDev Variance CoefVar
Minimum Q1
Data 1 100 73.24 1.41 14.13 199.62 19.29 31.43
64.72
Data 2 100 125.98 1.80 17.99 323.63 14.28 81.23
116.87
N for
Variable Median Q3 Maximum Range IQR Mode Mode
Skewness
Data 1 74.23 82.55 111.48 80.04 17.83 * 0 -0.10
Data 2 126.80 137.12 180.43 99.19 20.24 * 0 -
0.04
Variable Kurtosis
Data 1 0.67
Data 2 0.39
Correlation & Regression AnalysisCorrelation Coefficient and
P-Value
To calculate the correlation coefficient r and the P-value in
Minitab, use the following steps:
1. Click Stat and choose Basic Statistics and then Correlation.
(See below.)
2. Enter the two variables into the Variables box. (It makes no
difference in what order the columns are entered – the value for
r will be the same).
3. Click OK to display the results in the Session window.

Both the correlation coefficient (Pearson correlation) and the P-
value are displayed. Typical output is as follows:
Correlations: Data 1, Data 2
Pearson correlation of Data 1 and Data 2 = 0.836
P-Value = 0.000
Regression Equation and R-squared
To find the regression equation and R-squared value in Minitab,
use the following steps:
1. Click Stat and choose Regression and then Regression. (See
below.)
2. In the Response box, enter the variable that you think is
dependent on the other. (This is the y-variable.) In the
Predictor box, enter the independent variable. (This is the x-
variable).
3. Click OK to display the results in the Session window.
A partial sample output looks like this:
Regression Analysis: Data 2 versus Data 1
The regression equation is
Data 2 = 91.9 + 19.3 Data 1
Predictor Coef SE Coef T P
Constant 91.87 65.42 1.40 0.169
Data 1 19.290 2.170 8.89 0.000

S = 156.118 R-Sq = 69.9% R-Sq(adj) = 69.0%
Fitted Line Plot
To draw the scatterplot with the regression equation, use the
following steps:
1. Click Stat and choose Regression and then Fitted Line Plot.
2. In the Response (Y) box, enter the dependent (y) variable. In
the Predictor (X) box, enter the independent (x) variable.
3. The “Type of Regression Model” should be set to Linear.
4. Click OK to display the Fitted Line Plot.
The output will look like this:
Probability Distributions
Occasionally, a requirement may exist to generate random
observations from a specific probability distribution. This
manual looks at four distributions: Binomial, Poisson, Uniform,
and Normal.Binomial Probability Distribution
Below are the steps to calculate probability values for a
Binomial probability distribution:
1. Enter the values of the random variable for which you are
going to calculate the probabilities for in a column of the
worksheet. For example, if you were tossing a coin three times
and recording the number of heads, your random variable could
take on a value of 0, 1, 2, or 3. Therefore, you could enter
some (or all) of these values into column C1 (depending on
what probabilities you need to find).
2. Select the following: Calc –Probability Distributions –
Binomial.
3. Click on Probability. Enter the number of trials,n, and the

event probability,p. (The event probability is the probability of
getting a success on any one trial.) For example, if we are
tossing a coin three times and “heads” is considered a success,
then the number of trials is 3 and the event probability is 0.5.
4. Enter the Input column of the values of your random variable
(such as C1) from Step 1 and enter an Optional storage (output
column) for the probabilities (such as C2).
5. Click OK. The calculated probabilities will be entered in the
output column that you selected.
Input : x
Output : P(x)
If you need to add the results, click on Calc and choose Column
Statistics. Enter the column you want to sum, then click OK.
The result will be displayed in the session window.Poisson
Probability Distribution
Below are the steps to calculate probability values for a Poisson
probability distribution:
1. Enter the values for which you are going to calculate the
probability distribution in a column of the worksheet.
Poisson.
3. Click on Probability. Enter the mean.
If you need to add the results, click on Calc and choose Column

Statistics. Enter the column you want to sum, then click OK.
The result will be displayed in the session window.Uniform
Probability Distribution
Below are the steps to calculate probability values for a
Uniform probability distribution:
Uniform.
3. Click on Cumulative Probability. Enter the lower endpoint
and the upper endpoint.
If you are calculating a probability that x is less than some
number, the output column is the correct value to use.
If you are calculating a probability that x is greater than some
number, you need to subtract the output column from one to get
the correct value.
If you are calculating a probability that x is between two values,
subtract the two values in the output column so that the answer
is positive.
Normal Probability Distribution

Below are the steps to calculate probability values for a Normal
probability distribution:
Normal.
3. Click on Cumulative Probability. Enter the mean and
standard deviation.
If you are calculating a probability that x is less than some
number, the output column is the correct value to use.
If you are calculating a probability that x is greater than some
number, you need to subtract the output column from one to get
the correct value.
If you are calculating a probability that x is between two values,
subtract the two values in the output column so that the answer
is positive.
Alternate method for determining probabilities for a Normal
distribution:
1. Select the following: Graph –Probability Distribution Plot –
View Probability (last picture). Click OK.
2. Select Normal for the distribution and enter the values for the
meanand standard deviation.
3. In the same dialogue box, click on the Shaded Area tab.
4. Define Shaded area by X-value. Choose the correct tail and
enter in the x value (or the z score).

5. Click OK. Minitab will display the Normal curve with the
correct shaded region and the corresponding probability value.
This alternate method is nice because Minitab not only gives the
probability value, but it also shows the calculated area under the
curve. It allows you to find the area in either tail or in between
two values, and we don’t have to worry about subtracting
results like in the previous method.
As an example, IQ scores are normally distributed with a mean
of 100 and a standard deviation of 15. Suppose we want to find
the probability that a randomly selected person will have an IQ
score greater than 110 (i.e., find P(x > 110) ; right tail). We
would enter the following in Minitab:
Minitab would then display the following results and we would

see that the P(x > 110) = 0.2525
Confidence Intervals
This section provides information on the tools used to make
statistical inferences from sample data. The same commands
are used for confidence intervals and hypothesis testing but the
options selected make the difference.Confidence interval:
population mean, μ
The following procedure is used to create a confidence interval
for a population mean, μ.
Select Stat – Basic Statistics. Then choose one of the
following:
· 1-Sample Z (1Z) – use 1Z if you know the population
standard deviation, σ.
1. If you have original data, enter the column in Samples in
Columns. Otherwise click on the bubble for Summarized Data
and enter the sample size, mean, and population standard
deviation.
2. Click on Options and enter the desired Confidence level as a
percent (i.e. 95 for 95%).
3. Click OK twice.
The confidence interval will be displayed in the
Session window.
· 1-Sample t (1t) – use 1t if you do not know the population

and enter the sample size, mean, and sample standard deviation.
3. Click OK twice.
Session window.
· 2-Sample t (2t) – use 2t if you have two unpaired,
independent samples.
1. Click Samples in different columns and enter the two
columns into the First and Second boxes. Otherwise click on
the bubble for Summarized Data and enter the sample sizes,
means, and sample standard deviations.
3. Click OK twice.
Session window.
· Paired t (t-t) – use t-t if you have two paired samples.
1. Click Samples in columns and enter the two columns into the
Firstsample and Secondsample boxes.
3. Click OK twice.
Session window.Confidence interval: population proportion, p
· 1 Proportion (1P) – use 1P if you have the proportions with
only two classifications.

1. Click on Summarized data.
2. Enter the number of events (x) and the number of trials (n).
4. Click OK twice.
Session window.
Note: if you have the trials and percentage, you must multiply
the trials by the percent to determine the number of events
(successes). For example, if you had a sample of 1064 adults
and 53% believe in global warming, then the number that
believe in global warming would be 0.53(1064) = 563.92 or
564. (Here, you would enter 564 for the number of events and
1064 for the number of trials.)
· 2 Proportions (2P) – use 2P if you have two independent
populations with two classifications.
1. Click on Summarized data.
2. Enter the number of events and the number of trials for the
two independent populations.
percent. (i.e. 95 for 95%).
4. Click OK twice.
The confidence interval will be displayed in the Session
window.
Hypothesis Testing

This section deals with situations in which a claim is made
about a population parameter. There will be a null hypothesis
(H0) and an alternative hypothesis (H1 or HA). These
hypotheses should be stated prior to selecting the
command.Hypothesis Testing: population mean, μ
Select Stat – Basic Statistics. Then choose one of the
following:
· 1-Sample Z (1Z) – use 1Z if you know the population
and enter the sample size, mean, and population standard
deviation.
2. Click Perform Hypothesis test and enter the hypothesized
mean (the value in the null hypothesis, H0).
percent (i.e. Enter 95 for a hypothesis test with a 0.05
significance level.)
4. Change the Alternative to match the symbol in HA, the
alternative hypothesis.
5. Click OK twice.
The p-value will be displayed in the Session window.
· 1-Sample t (1t) – use 1t if you do not know the population
and enter the sample size, mean, and sample standard deviation.
mean (the value in the null hypothesis, H0).

5. Click OK twice.
· 2-Sample t (2t) – use 2t if you have two unpaired,
independent samples.
1. Click Samples in different columns and enter the two
columns into the First and Second boxes. Otherwise click on
the bubble for Summarized Data and enter the sample sizes,
means, and sample standard deviations.
2. Do Not check the box labeled “Assume equal variances”.
4. Enter 0 for the Test mean, then select the Alternative to
match the symbol in HA, the alternative hypothesis.
5. Click OK twice.
· Paired t (t-t) – use t-t if you have two paired samples.
1. Click Samples in columns and enter the two columns into the
Firstsample and Secondsample boxes.
percent (i.e. enter 95 for a hypothesis test with a 0.05
3. Enter 0 for the Test mean, then select the Alternative to

4. Click OK twice.
Hypothesis Testing: population proportion, p
· 1 Proportion (1P) – use 1P if you have the proportions with
only two classifications.
1. Click on Summarized data. Enter the number of events (x)
and the number of trials (n).
proportion (as a decimal).
5. Click OK twice.
· 2 Proportions (2P) – use 2P if you have two independent
populations with two classifications.
1. Click on Summarized data. Enter the number of events and
the number of trials for the two independent populations.
percent. (i.e. Enter 95 for a hypothesis test with a 0.05
3. Enter 0 for the Test difference, then select the Alternative to
4. Click on the box to use the pooled estimate of pfor the test.
5. Click OK twice.

Goto Table of Contents
Goto Table of Contents
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Regression Data and Project Information
TechHi is a retailer for a variety of electronics: stereos,
computers, networking equipment, and so on. They
communicate with customers solely through email and on-line
communications. The company spends a great deal of money
and staff time on these communications and management is
constantly examining data to ensure that the money is well
spent. The routinely collect a large amount of data on their
customers. The variables are
· Age: the customer’s age at the end of the current year
· Salary: annual salary of customer (individual salary if
customer is not married, combined annual salary of customer
and spouse if married)
· Children: the number of children living in the customer’s
household
· PrevSpent: the total amount, in dollars, the customer spent
with TechHi in the previous year
· Emails: the number of email communications sent to the
customer in the current year
· AmountSpent: the total amount of purchases made from
TechHi in the current year
You have been given data on n = 100 male customers. You are
to use the data to determine the best regression model for

predicting the amount spent in the current year using some or
all of the other variables as predictors. The work for the project
consists of several steps, outlined below.
· Week 1: Initial discussion of project and distribution of data
· Week 2: This portion centers on the response variable. You
will need to provide the mean, standard deviation, and five
number summary, as well as a minimum of two graphs. The
statistics and graphs will be used to address the shape of the
distribution. Submission should be a Word document. This
portion is worth 50 points.
· Week 4: Presentation of the best simple linear regression
model. You should include a discussion of the criterion used,
relevant Minitab output, and complete discussion of the fitted
line plot, regression equation, explained and unexplained
variability, and p-value for the test of significance for the
model. Submission should be a Word document. This portion is
worth 50 points.
· Week 5: Preliminary discussion of complete multiple
regression model. Appropriate items are below. Submission
should be a Word document. This is also worth 50 points.
· A discussion of the process that led to your choice of model –
relevant Minitab output included
· The p-value for the F-test of significance of the model. The
ANOVA table should be included
· Address the p-values for variables, including the relevant table
· Interpretations of the coefficients
· The improvement in fit, as measured by explained variation,
for the multiple regression model compared to the simple
regression model. Include here your thoughts on whether the
improvement in fit is large enough to justify the added
complexity of the model.
· Week 7: Presentation of your complete model. Include key
points from the previous steps, and a summary of your level of
satisfaction with the model. Submission should be a Word
document. This portion is worth 75 points.

Regression Data for Final Project G3 Stat 615.MPJUsin.docx

Regression Data for Final Project G3 Stat 615.MPJUsin.docx

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