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Quantitative Business

Analysis (QBA 501)

Block 1 Slides

Dr. Keith Whittingham

Module Layout

QBA 501

DescriptiveStatistics

Probability &Distributions

StatisticalInference

RegressionAnalysis

Data, Tables& Graphs

SummaryData

Types of DataGraphical

TechniquesPivot Tables

Cent ral Location Rank and Order Dispersion Boxplot s

Learning Objectives -Displaying Data

Understand types of data

Create and interpret histograms

Understand relationships among datathrough scatterplots

Understand time series plots

Manipulating data with pivot tables


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Types of Data

There are several ways to categorizedata.

Numerical (quantitative) versuscategorical (qualitative)

Cross-sectional versus time series

Numerical Data

Quantitative values

Real numbers

Arithmetic calculations valid

Examples

Income levels

Product weights

Sales revenue

Production rate

Numerical Data

Can be Continuous or Discrete

Continuous

Infinite number of possible values

No gaps in possible values

Discrete

Gaps in possible values


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Categorical Data

Categorical quality of an observation

Mutually exclusive

Collectively exhaustive

Examples

Eye color blue, brown, etc

Size of customer small, medium, large

Categorical Data

Can be Nominal or Ordinal

Nominal

Named category as variable

Name can be a number

Ordinal

Category identifies ranked order of values

Observations

An observation is a member of thepopulation or sample.

Each row corresponds to anobservation.

In this data set, each person representsan observation.


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Variables

A variable is a specific attribute beingobserved/measured.

Each column represents a variable.

In this data set, each of the six piecesof information about a person is avariable.

Numerical versus Categorical -- continued

Some options for this example are to:

code Gender (1 for male and 2 for female)

uncode Opinion variable

categorize the Age variable as young (34or younger), middle aged (from 35-59) andelderly (60 or older).

There is no right or wrong way Dealers choice.

Cross-sectional versus TimeSeries

Cross-sectional dataAll variables measured at one point in time snap shot

Coding.xls is cross-sectional; otherexamples?

Time-series data Measure one or more variables at

successive points in time.

Time-series examples?


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Module Layout

QBA 501




RegressionAnalysis


SummaryData




Frequency Tables andHistograms

Display how many observations fallwithin a category or range of values

Can be used for qualitative or quantitativevalues

Hard part is choosing categories(classes or bins)

Too many, or too few, and we losemeaningful information in the data.

Guidelines for bins/classes

Should be mutually exclusive

Should be collectively exhaustive

For Quantitative categories:

8-15 bins works best

Should have equal widths (roundnumbers better, e.g. 5, 10, 100, etc, )


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Frequency Distribution

Lets explore some common distributionshapes

Otis Elevators

Data consists of the diameter (ininches) of 400 elevator rails measuredby Otis Elevators.

The diameters range from a low ofapproximately 0.449 inch to a high ofapproximately 0.548 inch.

What type of distribution?


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Symmetric Histograms

A histogram is symmetric if it has asingle peak and looks approximately thesame to the left and right of the peak.

Bank Customer Arrivals

Data consists of the time betweencustomer arrivals - called interarrivaltimes - for all customers on a givenday.



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Positively Skewed Histograms

A histogram is positively skewed orskew ed to the right if it has a singlepeak and the values of the distributionextend much farther to the right of thepeak than to the left of the peak.

Accounting Midterm Grades

Data consists of the midterm grades fora large class of accounting students.



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Negatively Skewed Histograms

A histogram is negatively skew ed orskewed to the left if its longer tail ison the left.

Otis Elevators 2

Data consists of the diameters of allelevator rails produced on a single dayat Otis Elevators. Otis uses twomachines to produce elevator rails.

Too few bins


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Bimodal Distributions

Some histograms have two or morepeaks. This indicates that the datacomes from two or more distinctpopulations.

The result in this case is a bimodaldistribution.

Other multimodal distributions exist trimodal, etc.

Pie Chart

Cousin of the Histogram

Visualize frequency as a proportion ofthe entire data set.

Scatterplots

We are often interested in therelationship between two variables.

Plot a point for each observation, wherethe coordinates represent the values ofthe two variables.

The resulting graph is a scatterplot .


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Scatterplots

After constructing a scatterplot, we canexamine the scatter of points.

We look for any relationship between thetwo variables.

Direction: Is there a tendency for onevariable to move in concert with, or inopposition to, the other variable?

Strength: Are the points tightly clusteredaround an imaginary straight line? Or arethey more broadly scattered?

Time Series Plots

When we need to forecast future values of atime series, it is helpful to create a timeseries plot.

This is essentially a scatterplot, with the timeseries variable on the vertical axis and thetime itself on the horizontal axis.

Also, to make patterns in the data moreapparent, the points are usually connectedwith lines.

Analyzing a Time Series Plot

When looking at a time series plot weusually look for two things: Is there an observable trend or cycle? That

is, do the values of the series tend toincrease (an upward trend) or decrease (adownward trend) over time? Or cycle upand down?

Is there a seasonal pattern? For example,do the peaks or valleys for quarterly datatend to occur every fourth observation?


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Time Series Plots with twoVariables

Note that you can use different verticalscales for each variable.

This can yield time based relationshipsbetween variables in a manner similarto a scatterplot for cross-sectional data.

Module Layout

QBA 501




RegressionAnalysis


SummaryData




Pivot Tables

One of Excels most powerful tools.

Pivot tables allow us to slice and dicethe data.

Statisticians often refer to the resultingtables as contingency tables orcrosstabs.


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Creating a Pivot Table

Position the cursor in the data range.

On the Insert ribbon, select the PivotTable drop-down.

Select whether you want a pivot tableor chart.

With the chart, you get the table for free.

Creating a Pivot Table --continued

Next specify the range of the data set.

Then specify where you want to placethe pivot table and/or chart.


PivotTable button on the Insert ribbon.

Source and destination dialog box.


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There are two ways to proceed in thenext step.

Firstly, you can check the box on the pivottable field list to populate the table.

Alternatively, you can drag the variablenames to the appropriate field area in thepivot table field list.

Blank Pivot Table


The Field List window the destination labelsdepend on whether you chose a table orchart

Here is the correspondence: Axis Fields correspond to Row Labels

Legend Fields correspond to ColumnLabels


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Pivot Table Summary

The best way to learn the full power ofPivot Tables is to get in and play.

The automatic link to the charts is verypowerful, you can jump back and forthto view the impact of your actions.

Finally, you can manipulate pivot chartsjust like any other Excel charts.

Module Layout

QBA 501




RegressionAnalysis


SummaryData



Cen tr al Locat ion Ran k an d Or derDispersion &

AssociationBoxplots

Learning Objectives -Displaying Data

Understand types of data

Create and interpret histograms

Understand relationships among datathrough scatterplots

Understand time series plots

Manipulating data with pivot tables

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