CENTENNIAL HONORS COLLEGE
Western Illinois University
Undergraduate Research Day 2016
PosterPresentation
LogisticRegression
MatthewP.Rammelsberg
FacultyMentor:FeridunTasdan
Mathematics
Statisticiansuseregressiontodetermineifonesetofdataimpactsanother.Ifso,theycreatemodels
which describe the relationships between these data sets as functions. Such a function could predict
futurevaluesoftheimpactedsetbyplugginginconceptualvaluesfromtheother.Themostbasictype
ofregressionislinearregressionwhosefunctionstakeontheformY= 𝛼 + 𝛽𝑥 + 𝜀,whereYrepresents
the dependent (response) variable, x is an explanatory (independent) variable, and ε represents the
random errors that are assumed to be normal with a constant variance. However, linear regression
cannotbeappliedincaseswherethedependentvariableYconsistsofonlytwoelements(i.e.Y=(1,0).
Y=1canbedefinedasasuccessandY=0asafailure).Insuchcases,weneedlogisticregressionwhich
plugs x into a function that calculates the probability of success. On this poster, I provide more
explanationonwhatregressionis,howlogisticregressionisusedfordependentsetsthathaveonlytwo
elements, and a real-world example I made by analyzing support for Hillary Clinton’s presidential
campaign.Inthisexample,Iaskfourquestions:DoyoulikeHillaryClinton,howmanywomen/girlsare
in your immediate family, on average, how many hours do you spend on social media per week, and
whatisyourage?Aftersurveyingmanypeople,Iuselogisticregressiontoestimatetheprobabilityofa
success(someonesupportsHillaryClinton),oddsofsuccess(comparetonotsupportingHilaryClinton)
andrelatedhypothesistests.