QM Spring 2002 Business Statistics Bivariate Analyses for Qualitative Data

Student Objectives  Summarize regression analysis – Interpret regression statistics – Incorporate into report – Address questions concerning homework  Discuss why regression won’t work with qualitative data  Use crosstab approach for joint frequency distributions  Use PivotTable feature of Excel for creating crosstabs

Let’s Wrap Up Regression  Complete example from previous class  Review interpretations of regression statistics – Describe the relationship – Assess the validity  Summary of notation & terminology  Address questions concerning the homework – Expectations – Mechanics (e.g., copy/paste) – Other... ?

Results of Analysis of TV Time versus Age  Note: using complete data set  Results b 0 = hours/week b 1 = hours per year of age R 2 = 56% S yx = hours/week  Correlation (r): a single, multipurpose measure – Square root of R – Same sign as b 1 – R = – Summarizes the estimated strength of the relationship

Interpreting Regression Analyses (a)  Describing the relationship – Intercept (b 0 ): Base value for Y If it were possible for X to be 0, this is what Y would be – Slope (b 1 ): How much Y changes when X changes 1 unit The sensitivity of Y to changes in X (sometimes, the marginal value of X)

 Validity – R-Square (R 2 ): we know Y varies, but how much (i.e., what percentage) is attributable to the variation in X? – Standard error (S yx ): if we used the regression equation to predict Y, how much, on the average, should we expect to be wrong? Interpreting Regression Analyses (b)

Questions About the Homework?  Which data: – kivzdata.xls – All households, not just Ch.7  What analyses – Univariate Include: histogram and descriptive stats Variables: TV Time, Income – Bivariate Scatterplot (properly labeled) Regression statistics (the basic 4)  The report – Integrate charts with text – Nontechnical language  Other questions... ?

Regression, What Not to Do  Typical modeling errors – Reverse Y and X – Treat qualitative variables as quantitative  Use Excel shortcuts to create inflexible worksheets – Data analysis tool – Plot trend line

Now, Recall Analysis Depends on Data Type  Univariate: – Quanitative data: histograms, averages, etc. – Qualitative data: bar charts, proportions  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 Website Analytics Case  Pilot sample of major eCommerce sites  Note 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 business – Make vs buy – Apply to site development  What’s the research question here?

Examining the Question  Does “make vs buy” depend upon type of business model?  Start with simple frequency tables  Doesn’t tell us about how these variables are related  Need to go further: crosstab

Crosstabs: Many Flavors  Joint frequency: basis for developing the other three  Joint relative frequency (% of total) – Joint percentages – Margin percentages (same as univariate %)  Analyzing relationships – Row percentage – Column percentage

 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 analyze – With practice – Using basic probability concepts Crosstabs: Relationships

Using Excel’s PivotTable Feature for Crosstabs  Select the data, including headings  Click on Data | PivotTable  Click twice on Next  Click 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 Finish

Homework  Complete the KIVZ analysis/report  Development vs Model for WA case – Try to create crosstabulation – Think about whether a relationship exists