Page 31 - Regression Guideline

Important"Terms"You"Need"to"Know"
F&staDsDc:&&This"is"one"of"the"more"complicated"but"important"staJsJcal"concepts"to" understand."Things"vary"in"the"real"world."People"are"different"heights"and"weights;"some"live" a"long"Jme,"others"die"young;"some"nights"you"win"at"the"casino"and"others"you"lose"your" shirt;"some"properJes"are"worth"more"than"others."The"quesJon"in"each"circumstance"is"what" accounts"for"the"observed"variaJon."StaJsJcal"analysis"is"an"asempt"to"determine"when"the" variaJon"we"observe"can"be"reliably"predicted"by"some"known"set"of"characterisJcs"or" whether"the"observed"variaJon,"no"maser"how"large"or"seemingly"systemaJc,"is"due"to" unknown"or"random"and"therefore"unpredictable"effects."A"person"might"roll"a"set"of"snake" eyes"at"the"casino"an"improbably"large"number"of"Jmes"but"unless"the"dice"are"loaded,"each" roll"is"independent"of"the"next"and"the"series"of"throws"is"random."Blowing"on"the"dice,"or" wearing"a"specific"color"shirt,"or"hopping"on"one"foot"in"reality"had"no"effect"on"the"outcome."" In"the"context"of"property"appraisal,"the"FPstaJsJc"is"a"way"of"determining"the"probability"that" the"variaJon"in"sales"prices"seen"among"a"group"of"properJes"is"asributable"to"a"specific"set"of" predictors"is"reliable"and"predictable"or"whether"that"variaJon"is"more"likely"due"to" unmeasured"or"random"effects."The"FPtest"is"also"used"to"evaluate"whether"any"given"predictor" improves"the"fit"of"the"overall"model.""
" StaDsDcal&Significance."When"it"is"highly"unlikely"that"the"sales"price"variaJon"explained"is"due" to"chance"factors,"the"FPstaJsJc"and"model"are"said"to"be"staDsDcally&significant."In"a" regression"analysis"for"an"appraisal,"we"want"the"FPstaJsJc"for"the"model"to"be"staJsJcally" significant"at"the".05"level"(p"<".05)"or"lower."This"means"the"probability"the"property" characterisJcs"included"in"the"model"account"for"the"variaJon"in"sales"price"(the"R2)"purely"by" chance"would"happen"5%"of"the"Jme"or"less.""Because"that"is"such"a"small"likelihood,"we" conclude"the"model"is"“real”"and"the"predictors"as"a"set"are"reliable."Consequently,"knowing" the"values"for"these"predictors"allows"us"to"beser"esJmate"the"sales"price"than"if"we"just" guessed"the"mean"price"for"all"properJes"in"the"same"area"without"knowing"these" characterisJcs."In"addiJon,"we"also"want"each"predictor"to"be"staJsJcally"significant"because" this"means"that"its"associaJon"with"sales"price"is"reliable"and"not"due"to"chance."When"both" the"overall"regression"model"as"well"as"the"predictors"in"the"model"are"staJsJcally"significant," this"means"there"is"very"lisle"chance"the"predicted"sales"price"we"arrive"at"is"due"to"chance"or" random"factors.""
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