Independentvariablesarethefactorsthatcouldaffectyourdependentvariables.Forexample,apriceriseinthesecondquartercouldmakeanimpactonyoursalesfigures.
Youcanidentifyindependentvariableswiththefollowinglistofquestions:
Independentvariablesareoftenreferredtodifferentlyinregressiondependingonthepurposeoftheanalysis.Youmighthearthemcalled:
Explanatoryvariables
Explanatoryvariablesarethosewhichexplainaneventoranoutcomeinyourstudy.Forexample,explainingwhyyoursalesdroppedorincreased.
Predictorvariables
Experimentalvariables
Thesearevariablesthatcanbemanipulatedorchangeddirectlybyresearcherstoassesstheimpact.Forexample,assessinghowdifferentproductpricing($10vs$15vs$20)willimpactthelikelihoodtopurchase.
Subjectvariables(alsocalledfixedeffects)
Subjectvariablescan’tbechangeddirectly,butvaryacrossthesample.Forexample,age,gender,orincomeofconsumers.
Unlikeexperimentalvariables,youcan’trandomlyassignorchangesubjectvariables,butyoucandesignyourregressionanalysistodeterminethedifferentoutcomesofgroupsofparticipantswiththesamecharacteristics.Forexample,‘howdopricerisesimpactsalesbasedonincome’
Carryingoutregressionanalysis
Soregressionisabouttherelationshipsbetweendependentandindependentvariables.Buthowexactlydoyoudoit
Assumingyouhaveyourdatacollectiondonealready,thefirstandforemostthingyouneedtodoisplotyourresultsonagraph.Doingthismakesinterpretingregressionanalysisresultsmucheasierasyoucanclearlyseethecorrelationsbetweendependentandindependentvariables.
Let’ssayyouwanttocarryoutaregressionanalysistounderstandtherelationshipbetweenthenumberofadsplacedandrevenuegenerated.
OntheY-axis,youplacetherevenuegenerated.OntheX-axis,thenumberofdigitalads.Byplottingtheinformationonthegraph,anddrawingaline(calledtheregressionline)throughthemiddleofthedata,youcanseetherelationshipbetweenthenumberofdigitaladsplacedandrevenuegenerated.
Thisregressionlineisthelinethatprovidesthebestdescriptionoftherelationshipbetweenyourindependentvariablesandyourdependentvariable.Inthisexample,we’veusedasimplelinearregressionmodel.
Asimplelinearmodelusesasinglestraightlinetodeterminetherelationshipbetweenasingleindependentvariableandadependentvariable.
Thisregressionmodelismostlyusedwhenyouwanttodeterminetherelationshipbetweentwovariables(likepriceincreasesandsales)orthevalueofthedependentvariableatcertainpointsoftheindependentvariable(forexamplethesaleslevelsatacertainpricerise).
Whilelinearregressionisuseful,itdoesrequireyoutomakesomeassumptions.
Forexample,itrequiresyoutoassumethat:
Asthenamesuggests,multipleregressionanalysisisatypeofregressionthatusesmultiplevariables.Itusesmultipleindependentvariablestopredicttheoutcomeofasingledependentvariable.Ofthevariouskindsofmultipleregression,multiplelinearregressionisoneofthebest-known.
Multiplelinearregressionisacloserelativeofthesimplelinearregressionmodelinthatitlooksattheimpactofseveralindependentvariablesononedependentvariable.However,likesimplelinearregression,multipleregressionanalysisalsorequiresyoutomakesomebasicassumptions.
Forexample,youwillbeassumingthat:
Anexampleofmultiplelinearregressionwouldbeananalysisofhowmarketingspend,revenuegrowth,andgeneralmarketsentimentaffectthesharepriceofacompany.
Withmultiplelinearregressionmodelsyoucanestimatehowthesevariableswillinfluencetheshareprice,andtowhatextent.
Multivariatelinearregressioninvolvesmorethanonedependentvariableaswellasmultipleindependentvariables,makingitmorecomplicatedthanlinearormultiplelinearregressions.However,thisalsomakesitmuchmorepowerfulandcapableofmakingpredictionsaboutcomplexreal-worldsituations.
Forexample,ifanorganizationwantstoestablishorestimatehowtheCOVID-19pandemichasaffectedemployeesinitsdifferentmarkets,itcanusemultivariatelinearregression,withthedifferentgeographicalregionsasdependentvariablesandthedifferentfacetsofthepandemicasindependentvariables(suchasmentalhealthself-ratingscores,proportionofemployeesworkingathome,lockdowndurationsandemployeesickdays).
Throughmultivariatelinearregression,youcanlookatrelationshipsbetweenvariablesinaholisticwayandquantifytherelationshipsbetweenthem.Asyoucanclearlyvisualizethoserelationships,youcanmakeadjustmentstodependentandindependentvariablestoseewhichconditionsinfluencethem.Overall,multivariatelinearregressionprovidesamorerealisticpicturethanlookingatasinglevariable.
However,becausemultivariatetechniquesarecomplex,theyinvolvehigh-levelmathematicsthatrequireastatisticalprogramtoanalyzethedata.
Logisticregressionmodelstheprobabilityofabinaryoutcomebasedonindependentvariables.
So,whatisabinaryoutcomeIt’swhenthereareonlytwopossiblescenarios,eithertheeventhappens(1)oritdoesn’t(0).e.g.yes/nooutcomes,pass/failoutcomes,andsoon.Inotherwords,iftheoutcomecanbedescribedasbeingineitheroneoftwocategories.
Logisticregressionmakespredictionsbasedonindependentvariablesthatareassumedorknowntohaveaninfluenceontheoutcome.Forexample,theprobabilityofasportsteamwinningtheirgamemightbeaffectedbyindependentvariableslikeweather,dayoftheweek,whethertheyareplayingathomeorawayandhowtheyfaredinpreviousmatches.
Whataresomecommonmistakeswithregressionanalysis
Usingthewrongdataorthewrongassumptionscanresultinpoordecision-making,leadtomissedopportunitiestoimproveefficiencyandsavings,and—ultimately—damageyourbusinesslongterm.
Whenrunningregressionanalysis,beitasimplelinearormultipleregression,it’sreallyimportanttocheckthattheassumptionsyourchosenmethodrequireshavebeenmet.Ifyourdatapointsdon’tconformtoastraightlineofbestfit,forexample,youneedtoapplyadditionalstatisticalmodificationstoaccommodatethenon-lineardata.Forexample,ifyouarelookingatincomedata,whichscalesonalogarithmicdistribution,youshouldtaketheNaturalLogofIncomeasyourvariablethenadjusttheoutcomeafterthemodeliscreated.
It’sawell-wornphrasethatbearsrepeating–correlationdoesnotequalcausation.Whilevariablesthatarelinkedbycausalitywillalwaysshowcorrelation,thereverseisnotalwaystrue.Moreover,thereisnostatisticthatcandeterminecausality(althoughthedesignofyourstudyoverallcan).
Ifyouobserveacorrelationinyourresults,suchasinthefirstexamplewegaveinthisarticlewheretherewasacorrelationbetweenleadsandsales,youcan’tassumethatonethinghasinfluencedtheother.Instead,youshoulduseitasastartingpointforinvestigatingtherelationshipbetweenthevariablesinmoredepth.
Beforeyouuseanykindofstatisticalmethod,it’simportanttounderstandthesubjectyou’reresearchingindetail.Doingsomeansyou’remakinginformedchoicesofvariablesandyou’renotoverlookingsomethingimportantthatmighthaveasignificantbearingonyourdependentvariable.
Benefitsofusingregressionanalysis
Thereareseveralbenefitstousingregressionanalysistojudgehowchangingvariableswillaffectyourbusinessandtoensureyoufocusontherightthingswhenforecasting.
Herearejustafewofthosebenefits:
Regressionanalysisiscommonlyusedwhenforecastingandforwardplanningforabusiness.Forexample,whenpredictingsalesfortheyearahead,anumberofdifferentvariableswillcomeintoplaytodeterminetheeventualresult.
Regressionanalysiscanhelpyoudeterminewhichofthesevariablesarelikelytohavethebiggestimpactbasedonpreviouseventsandhelpyoumakemoreaccurateforecastsandpredictions.
Usingaregressionequationabusinesscanidentifyareasforimprovementwhenitcomestoefficiency,eitherintermsofpeople,processes,orequipment.
Forexample,regressionanalysiscanhelpacarmanufacturerdetermineordernumbersbasedonexternalfactorsliketheeconomyorenvironment.
Usingtheinitialregressionequation,theycanuseittodeterminehowmanymembersofstaffandhowmuchequipmenttheyneedtomeetorders.
Improvingprocessesorbusinessoutcomesisalwaysonthemindsofownersandbusinessleaders,butwithoutactionabledata,they’resimplyrelyingoninstinct,andthisdoesn’talwaysworkout.
Thisisparticularlytruewhenitcomestoissuesofprice.Forexample,towhatextentwillraisingtheprice(andtowhatlevel)affectnextquarter’ssales
There’snowaytoknowthiswithoutdataanalysis.Regressionanalysiscanhelpprovideinsightsintothecorrelationbetweenpricerisesandsalesbasedonhistoricaldata.
Marketingandadvertisingspendingarecommontopicsforregressionanalysis.Companiesuseregressionwhentryingtoassessthevalueofadspendandmarketingspendonrevenue.
Atypicalexampleisusingaregressionequationtoassessthecorrelationbetweenadcostsandconversionsofnewcustomers.Inthisinstance,
Theanalysisisrelativelystraightforward—usinghistoricaldatafromanadaccount,wecanusedailydatatojudgeadspendvsconversionsandhowchangestothespendaltertheconversions.
Byassessingthisdataovertime,wecanmakepredictionsnotonlyonwhetherincreasingadspendwillleadtoincreasedconversionsbutalsowhatlevelofspendingwillleadtowhatincreaseinconversions.ThiscanhelptooptimizecampaignspendandensuremarketingdeliversgoodROI.
Thisisanexampleofasimplelinearmodel.Ifyouwantedtocarryoutamorecomplexregressionequation,wecouldalsofactorinotherindependentvariablessuchasseasonality,GDP,andthecurrentreachofourchosenadvertisingnetworks.
Byincreasingthenumberofindependentvariables,wecangetabetterunderstandingofwhetheradspendisresultinginanincreaseinconversions,whetherit’sexertinganinfluenceincombinationwithanothersetofvariables,orifwe’redealingwithacorrelationwithnocausalimpact–whichmightbeusefulforpredictionsanyway,butisn’taleverwecanusetoincreasesales.
Usingthispredictedvalueofeachindependentvariable,wecanmoreaccuratelypredicthowspendwillchangetheconversionrateofadvertising.
Regressionanalysisisanimportanttoolwhenitcomestobetterdecision-makingandimprovedbusinessoutcomes.Togetthebestoutofit,youneedtoinvestintherightkindofstatisticalanalysissoftware.
Thebestoptionislikelytobeonethatsitsattheintersectionofpowerfulstatisticalanalysisandintuitiveeaseofuse,asthiswillempowereveryonefrombeginnerstoexpertanalyststouncovermeaningfromdata,identifyhiddentrendsandproducepredictivemodelswithoutstatisticaltrainingbeingrequired.
Tohelppreventcostlyerrors,chooseatoolthatautomaticallyrunstherightstatisticaltestsandvisualizationsandthentranslatestheresultsintosimplelanguagethatanyonecanputintoaction.
Withsoftwarethat’sbothpowerfulanduser-friendly,youcanisolatekeyexperiencedrivers,understandwhatinfluencesthebusiness,applythemostappropriateregressionmethods,identifydataissues,andmuchmore.
WithQualtrics’StatsiQ,youdon’thavetoworryabouttheregressionequationbecauseourstatisticalsoftwarewillruntheappropriateequationforyouautomaticallybasedonthevariabletypeyouwanttomonitor.Youcanalsouseseveralequations,includinglinearregressionandlogisticregression,togaindeeperinsightsintobusinessoutcomesandmakemoreaccurate,data-drivendecisions.