DATA ANALYSIS III MKT525

Multiple Regression Simple regression:DV = a + bIV Multiple regression: DV = a + b 1 IV 1 + b 2 IV 2 + …b n IV n b i = weight associated with each IV i

Multiple regression: data

How do you get a small standard error for regression coefficient? Large sample Large variability in values of IV’s Reliable DV No multi-collinearity

Example Shoe mfr. wants to predict sales for each of 122 retail stores. DV = sales ($000) IV 1 = population of area ( x000) IV 2 = likelihood of customers purchasing IV 3 = median income ($000) DV = IV V IV 3 R 2 =.49

When to use multiple regression There is one DV and more than one IV You want to predict or explain DV as a function of the IV’s Both DV and IV’s are interval or ratio scale (IV can be nominal or ordinal if you use ‘dummy coding’) Relationship between DV and each IV is linear IV’s are relatively independent of each other

Multi-Collinearity If IV’s not independent, regression coefficients will not be good predictors of DV Can still predict DV but you will have a problem if you want to find the relative importances of IV’s Symptoms of multi-collinearity

What to look for in a regression What is the R 2 ? Is regression model significant? Which coefficients are significantly different from zero? How does this model predict the DV? What are the relative importances of the IV’s? Is there evidence of multi-collinearity? Was a hold-out sample used?

Analysis of Variance (ANOVA) Use to analyze differences among more than two groups Use to analyze differences between 2 or more groups on more than one variable at a time Do different levels of a variable come from the same population or do they come from different populations?

Same response for all No. CDs. Freq.

People give different responses No. CDs Freq.

Example of CDs Total variance = systematic var.+ error var. Does number of CDs vary by gender? Total variance = gender var. + error var. Does number of CDs vary by gender and age? Total variance= gender var.+age var. +error var. Ho = No difference in no. CDs bought by men vs. women nor by teens vs. adults.

Terms used in ANOVA Variance F-ratio Sum of squares Mean square ANOVA table Source SS df MS F-ratio Between SS b MS b MS b /MS w Within SS w MS w Total SS t

MS and F-ratio MSw = estimate of population variance; includes sample error MSb = estimate of population variance; includes sample error + between-group variance F-ratio = MSb/MSw

Example of 1-way ANOVA

ANOVA of 3 promotions in four cities for each promotion

Factorial Design: 3 promos + 2 levels of advertising

ANOVA for factorial design

No Interaction Heavy media wt. Light media wt. CouponSample C&S

Interaction Heavy media wt. Light media wt. CouponSample C&S