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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
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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 b0 = 5.581 hours/week b1 = 0.522 hours per year of age R2 = 56% Syx = 6.924 hours/week • Correlation (r): a single, multipurpose measure • Square root of R • Same sign as b1 • R = +0.75 • Summarizes the estimated strength of the relationship
Interpreting Regression Analyses (a) • Describing 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)
Interpreting Regression Analyses (b) • Validity • 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?
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
Crosstabs: Relationships • 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
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