QM 2113 - Spring 2002QM 2113 - Spring 2002

Business StatisticsBusiness Statistics

Bivariate Analyses Bivariate Analyses for Qualitative for Qualitative

DataData

Student ObjectivesStudent Objectives

Summarize regression analysisSummarize regression analysis– Interpret regression statistics– Incorporate into report– Address questions concerning homework

Discuss why regression won’t work Discuss why regression won’t work with qualitative datawith qualitative data

Use crosstab approach for joint Use crosstab approach for joint frequency distributionsfrequency distributions

Use PivotTable feature of Excel for Use PivotTable feature of Excel for creating crosstabscreating crosstabs

Let’s Wrap Up Let’s Wrap Up RegressionRegression

Complete example from previous classComplete example from previous class Review interpretations of regression Review interpretations of regression

statisticsstatistics– Describe the relationship– Assess the validity

Summary of notation & terminologySummary of notation & terminology Address questions concerning the Address questions concerning the

homeworkhomework– Expectations– Mechanics (e.g., copy/paste)– Other . . . ?

Results of Analysis Results of Analysis of TV Time versus of TV Time versus

AgeAge Note: using complete data setNote: using complete data set ResultsResults

b0 = 5.581 hours/weekb1 = 0.522 hours per year of ageR2 = 56%Syx = 6.924 hours/week

Correlation Correlation (r)(r): a single, multipurpose : a single, multipurpose measuremeasure– Square root of R– Same sign as b1

– R = +0.75– Summarizes the estimated strength of the

relationship

Interpreting Interpreting Regression Analyses Regression Analyses

(a)(a) Describing the relationshipDescribing the relationship

– Intercept (b0):• Base value for Y• If it were possible for X to be 0, this is what Y

would be

– Slope (b1):• How much Y changes when X changes 1 unit• The sensitivity of Y to changes in X

(sometimes, the marginal value of X)

ValidityValidity– R-Square (R2): we know Y varies, but

how much (i.e., what percentage) is attributable to the variation in X?

– Standard error (Syx): if we used the regression equation to predict Y, how much, on the average, should we expect to be wrong?

Interpreting Interpreting Regression Analyses Regression Analyses

(b)(b)

Questions About the Questions About the Homework?Homework?

Which data: Which data: – kivzdata.xls– All households, not just Ch.7

What analysesWhat analyses– Univariate

• Include: histogram and descriptive stats• Variables: TV Time, Income

– Bivariate• Scatterplot (properly labeled)• Regression statistics (the basic 4)

The reportThe report– Integrate charts with text– Nontechnical language

Other questions . . . ?Other questions . . . ?

Regression, What Regression, What Not to DoNot to Do

Typical modeling errorsTypical modeling errors– Reverse Y and X– Treat qualitative variables as

quantitative Use Excel shortcuts to create Use Excel shortcuts to create

inflexible worksheetsinflexible worksheets– Data analysis tool– Plot trend line

Now, Recall Analysis Now, Recall Analysis Depends on Data Depends on Data

TypeType Univariate:Univariate:

– Quanitative data: histograms, averages, etc.– Qualitative data: bar charts, proportions

Bivariate:Bivariate:– Both variables quantitative

• Scatterplots• Regression analysis

– Either or both variables qualitative• Contingency tables, aka:

– PivotTables (Excel)– Crosstabulations

• Chi-square analysis (beyond our scope)

Let’s Look at the Let’s Look at the Website Analytics Website Analytics

CaseCase Pilot sample of major eCommerce sitesPilot sample of major eCommerce sites Note Internet business modelsNote Internet business models

– Virtual storefront (e.g., Amazon)– Content provider (e.g., WSJ)– Auction (e.g., eBay)– Several others, but these are the top three

Major decision common in businessMajor decision common in business– Make vs buy– Apply to site development

What’s the research question here?What’s the research question here?

Examining the Examining the QuestionQuestion

Does “make vs buy” depend Does “make vs buy” depend upon type of business model?upon type of business model?

Start with simple frequency Start with simple frequency tablestables

Doesn’t tell us about how Doesn’t tell us about how these variables are relatedthese variables are related

Need to go further: crosstabNeed to go further: crosstab

Crosstabs:Crosstabs:Many FlavorsMany Flavors

Joint frequency: basis for Joint frequency: basis for developing the other threedeveloping the other three

Joint relative frequency (% of Joint relative frequency (% of total)total)– Joint percentages– Margin percentages (same as univariate %)

Analyzing relationshipsAnalyzing relationships– Row percentage– Column percentage

Relationship?Relationship?– If so, % of observations in given

category of primary variable should differ substantially across categories of explanatory variable

– That is, depending upon type of table,• Row % values differ down a given column, or• Column % values across a given row

Easier to analyzeEasier to analyze– With practice– Using basic probability concepts

Crosstabs: Crosstabs: RelationshipsRelationships

Using Excel’s Using Excel’s PivotTable Feature PivotTable Feature

for Crosstabsfor Crosstabs Select the data, including headingsSelect the data, including headings Click on Data | PivotTableClick on Data | PivotTable Click twice on NextClick twice on Next Click on LayoutClick on Layout

– Drag Development to row– Drag Model to column– Drag either to data– Double click on data button

• Select Count, then click on Options• In Show Data As, select % of Total• Click on OK

– Click on OK Click on FinishClick on Finish

HomeworkHomework

Complete the KIVZ Complete the KIVZ analysis/reportanalysis/report

Development vs Model for WA Development vs Model for WA casecase– Try to create crosstabulation– Think about whether a relationship

exists