Doing Statistics for Business Data, Inference, and Decision Making Marilyn K' Pelosi Theresa M' Sand

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Doing Statistics for Business Data, Inference,
and Decision MakingMarilyn K. PelosiTheresa M.
Sandifer
Chapter 5 Analyzing Bivariate Data

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Doing Statistics for Business

• Chapter 5 Objectives
• Bivariate Qualitative Data
• Contingency Tables
• Clustered Stacked Bar Charts
• Identifying Quantitative Relationships
  Scatter Plots
• The Least-squares Line

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Doing Statistics for Business

• A Contingency Table is a table whose
• rows represent the possible values of
• one variable and whose columns
• represent the possible values for a
• second variable. The entries in the table
• are the number of times that each pair
• of values occurs.

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Doing Statistics for Business

• TRY IT NOW!
• Quality Problems
• Creating a Contingency Table
• A company that manufactures cardboard boxes is
  trying to
• understand some of their quality problems. They
  have analyzed some
• data and determined that their major defects are
  Printing, Color and
• Skewness (how square the box is). Further
  attempts to pinpoint the
• problems have resulted in many opinions and
  finger pointing about
• responsibility. They decide to collect some
  additional data on defect
• type and the shift during which production
  occurred.

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Doing Statistics for Business

• TRY IT NOW!
• Quality Problems
• Creating a Contingency Table (cont)
• The data (sorted by defect type) are as follows

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Doing Statistics for Business

• TRY IT NOW!
• Quality Problems
• Creating a Contingency Table (cont)
• Create a relative frequency contingency table for
  the data.
• What percentage of the defects were color?
• Does there appear to be any credence tot he claim
  that the majority of the
• defects occur on the third shift?

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Doing Statistics for Business
Figure 5.1 Two bar charts representing
a contingency table
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Doing Statistics for Business

• In a Clustered Bar Chart, the bars for
• one variable are grouped according to
• the values of the other qualitative
• variables.

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Doing Statistics for Business
Figure 5.2 Example of a Clustered Bar Chart
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Doing Statistics for Business

• TRY IT NOW!
• Quality Problems
• Creating a Clustered Bar Chart
• The management of the company that manufactures
  cardboard boxes
• decide to have a meeting with the crews about the
  quality problems. The
• managers decide that a graphical display of the
  data is the best way to
• convey the information they have obtained and
  that they want to display
• the crew data for each of the quality defects.

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Doing Statistics for Business

• TRY IT NOW!
• Quality Problems
• Creating a Clustered Bar Chart (cont)
• Create a clustered bar chart that display the
  percent defects for each shift
• using the quality problems as the categories for
  the x axis.

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Doing Statistics for Business

• TRY IT NOW!
• Quality Problems
• Creating a Clustered Bar Chart (cont)
• Which shift contributes the largest percentage of
  color defects? The least
• percentage?
• What do you notice about the skewness defects?

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Doing Statistics for Business

• In a Stacked Bar Chart the data for the
• selected variable are represented as a
• percentage of the total for each category
• of the second variable. Each value of
• the selected variable is represented in a
• different way and the bars are stacked
• to total 100.

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Doing Statistics for Business
Figure 5.3 Stacked Bar Chart
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Doing Statistics for Business

• TRY IT NOW!
• Quality Problems
• Creating a Stacked Bar Chart
• The company that manufactures cardboard boxes
  decides to create
• a graphical display of the data to show to the
  employees. What the
• company wants to do is to display type of defect
  as a percentage of
• total defects for each shift. It is hoped that
  these data will help each shift
• concentrate on its own priorities. The
  contingency table for the defect is
• shown on the following slide.

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Doing Statistics for Business

• TRY IT NOW!
• Quality Problems
• Creating a Stacked Bar Chart (cont)
• Modify the contingency table to display defect
  types as a percentage of
• total defects for each shift.

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Doing Statistics for Business

• TRY IT NOW!
• Quality Problems
• Creating a Stacked Bar Chart (cont)
• Create a stacked bar chart for the data.
• Which defect type should each crew concentrate
  on? Why?

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Doing Statistics for Business

• In a Scatter Plot an axis is used to
• represent each of the variables and the
• data are plotted as points on the graph.
• Typically, the independent variable is
• plotted on the x axis and the dependent
• variable is plotted on the y axis.

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Doing Statistics for Business
Figure 5.4 Scatter Plot
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Doing Statistics for Business

• TRY IT NOW!
• Airline Fares
• Creating a Scatter Plot
• A travel agency was interested in knowing how
  airline fares were
• related to the length of the flight in miles.
  The agency hypothesized
• that the longer the flight, the more the
  airfare. The following data were
• collected

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Doing Statistics for Business

• TRY IT NOW!
• Airline Fares
• Creating a Scatter Plot (cont)
• Which variable is the dependent variable and
  which is the independent
• variable?
• Make a scatter plot of the data.
• From your plot, do you think that the travel
  agencys hypothesis was
• correct? Why or why not?

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Doing Statistics for Business
Figure 5.6 Scatter Plot Indicating no
Relationship Between Two Variables
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Doing Statistics for Business

• TRY IT NOW!
• Starting Salaries Math Courses
• Finding the Least-Squares Line
• The Career Planning office of a large university
  is interested in knowing
• whether there is a relationship between the
  starting salary of graduates
• and the number of mathematics courses the
  graduates had taken as
• students. The Career Planning office goes
  through the records for the
• last year and finds the following data.

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Doing Statistics for Business

• TRY IT NOW!
• Starting Salaries Math Courses
• Finding the Least-Squares Line (cont)
• Which variable is the independent variable? The
  dependent variable?

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Doing Statistics for Business

• TRY IT NOW!
• Starting Salaries Math Courses
• Finding the Least-Squares Line (cont)
• Use a grid to create a scatter plot of the data.
• Do you think that there is a linear relationship
  between the number of
• math courses taken and the starting salary? If
  so, describe the
• relationship.

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Doing Statistics for Business

• Discovery Exercise 5.1
• Discovering Relationships
• 1. The data below represent data taken on the
  number
• of weeks that a student was enrolled in a speed
  reading program
• and the speed gain in words per minute that the
  student has experienced

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Doing Statistics for Business

• Discovery Exercise 5.1
• Discovering Relationships (cont)
• 2. Plot the data on graph paper. Be sure to
  label your axes
• and to construct the graph so that it uses most
  of the paper.
• 3. Draw a straight line through the points that
  you think best represent the
• relationship between x and y. What criteria did
  you use for drawing the
• line you selected?

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Doing Statistics for Business

• The Least Squares technique finds the
• equation of the line that minimizes the
• sum of the squared errors between the
• actual data points and the line.

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Doing Statistics for Business
Figure 5.7 Deviations Between the Data
Points and the Line
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Doing Statistics for Business

• The distance between the predicted value
• of Y, called the deviation or error. The
• deviation, e, is equal to - y.

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Doing Statistics for Business

• TRY IT NOW!
• Starting Salaries and Math Courses
• Finding the Least-Squares Line
• The Career Planning office at the university
  wants to use
• least squares to find the equation that relates
  the number of math
• courses taken and starting salary. The data are
• Number of math courses Starting Salary ()
• 1 26,284
• 1 25,470
• 2 26,777
• 3 27,269
• 4 28,553
• 6 30,054

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Doing Statistics for Business

• TRY IT NOW!
• Starting Salaries and Math Courses
• Finding the Least-Squares Line (cont)
• (a) Find the equation for the least-squares line
  for the data.
• (b) Explain what the least-squares line tells the
  Career Planning Office about math courses and
  starting salary.

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Doing Statistics for Business

• TRY IT NOW!
• Starting Salaries and Math Courses
• Finding the Least-Squares Line
• Once the least-squares equation is obtained the
  Career Planning
• Office wants to see whether the equation does a
  good job of predicting
• starting salary for a given number of math
  courses.
• Plot the data and the least-squares line on the
  same graph.

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Doing Statistics for Business

• TRY IT NOW!
• Starting Salaries and Math Courses
• Finding the Least-Squares Line
• Use the equation you just found to predict the
  starting salary
• of a person who takes 2 mathematics courses. Do
  the same thing
• for the starting salary of a person who takes 5
  mathematics courses.
• Do you think the predictions from the
  least-squares line are useful? Why
• or why not?
• Is what you just did interpolation or
  extrapolation?

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Doing Statistics for Business

• TRY IT NOW!
• Starting Salaries and Math Courses
• Finding the Least-Squares Line (cont)
• Now use the equation of the least-squares line to
  predict the
• starting salary of a person who takes no math
  courses. Do the
• same thing for a person who takes 10 math
  courses.
• Do you think these predictions are valid? Why or
  why not?

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Doing Statistics for Business

• Creating Contingency Tables in Excel
• 1. From the Data menu, select PivotTable and
  Pivot Chart Report .
• 2. Since you have already highlighted the range
  that contains your data, you can just proceed by
  clicking Nextgt.
• 3. Indicate where you want the Pivot table to
  appear and click the button labeled Layout.

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Doing Statistics for Business

• Creating Contingency Tables in Excel
• 4. Drag the field box for Rank to the area
  marked Row and the field box for School to the
  area marked Column. Now drag the field box for
  either Rank or School into the area marked Data.
• 5. Click on Next and tell Excel where you want
• the table to appear either in the current
  worksheet
• or in a new worksheet.
• 6. Finally, click on Finish.

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• Figure 5.10 Contingency Table of Rank and School

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Doing Statistics for Business

• The basics of creating a chart in Excel,
• using the Chart Wizard.
• 1. Highlight the data (Frequency table) that you
  want to graph.
• 2. Invoke the Chart Wizard by clicking on the
  icon on the toolbar.
• 3. Follow the directions and hints from the Chart
  Wizard.
• 4. Edit the graph to include any other features
  or changes you want.

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Doing Statistics for Business

• Creating Clustered Bar Charts in in Excel
• 1. Highlight just a portion of the pivot table by
  copying it to another location in the worksheet
  using the Paste Special command. To do this click
  on the lower right hand corner of the table and
  highlight it. Select Copy from the Edit menu.
  Then, click on the location for the copy and
  select Paste Special. In the Paste section,
  click on the radio button for Values and in the
  Operation section, select None. Click OK.

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Doing Statistics for Business

• Creating Clustered Bar Charts in in Excel
• (cont)
• 2. Highlight the copy of the table, being careful
  not to highlight the Grand Total row or column.
  Then start the Chart Wizard and select Column as
  the type of chart and clustered chart as the
  sub-type.
• 3. Click Next twice to get to the Options step
  add titles and make any desired formatting
  changes.
• 4. Click Next to indicate where you want the
  chart to be located and then click Finish.

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• Figure 5.14 Clustered Bar Chart

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• Creating Stacked Bar Charts in in Excel
• 1. Highlight the rows of the pivot table, being
  careful not to include the Grand Total row and
  column and start the Chart Wizard.
• 2. Select Column as the chart type and 100
  Stacked Column as the sub-type.
• 3. Click Next twice to get to the Options step
  put in titles and any other formatting changes
  that you want.
• 4. Click Next, enter the location for the chart,
  and click Finish to display the chart.

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• Figure 5.17 Stacked Bar Chart

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• Analyzing Quantitative Bivariate Data
• in Excel
• 1. Highlight the range of the data and start the
  Chart Wizard. Select XY (Scatter) as the chart
  type and Scatter no lines) for the subtype.
• 2. Select Nextgt twice to get to the Chart Options
  dialog box put in titles and any other
  formatting changes that you want.
• 3. Select Nextgt to tell Excel where to locate the
  chart and click Finish to display the chart.

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• Figure 5.20 Finished Scatter Plot

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• Adding the Least-Squares Line to Your
• Scatter Plot
• 1. Click on any one of the points in the scatter
  plot to highlight them all.
• 2. From the Chart menu, select Add Trendline. The
  Add Trendline dialog box will open.
• 3. In the Trend/Regression section, highlight
  Linear.
• 4. Click on the Options tab and click the box
  labeled Display equation on chart.
• 5. Click OK.

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• Figure 5.24 Scatter Plot with Least-Squares
  Line

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Doing Statistics for Business

• Chapter 5 Summary
• In this chapter you have learned
• Some methods for looking at how two variables are
  related.
• There are graphical methods, such as stacked bar
  charts, clustered bar charts, and scatter plots.
• There are quantitative methods, such as
  least-squares analysis.