Page 32 - Regression Guideline

Important"Terms"You"Need"to"Know"
Linear®ression:"Is"a"staJsJcal"technique"that"asempts"to"model"the"relaJonship"between" one"or"more"predictor"variables"with"one"independent"variable"by"esJmaJng"a"linear"equaJon" based"on"observed"data."The"model"is"linear"because"it"assumes"either"a"constantly"increasing" (posiJve)"or"decreasing"(negaJve)"relaJonship"between"the"set"of"predictors"and"the" dependent"variable."For"example,"in"a"linear"regression"model,"as"square"footage"increases," the"sales"price"is"assumed"to"increase"at"a"constant"rate"as"in"our"earlier"example"where"sales" price"increased"$100"for"every"1"foot"increase"in"square"feet."A"linear"relaJonship"is"usually"a" safe"assumpJon"for"most"applicaJons"of"regression"modeling"to"property"appraisal."There" could"be"rare"instances"such"as"at"the"high"end"of"the"market,"however,"where"increasing" square"footage"a^er"a"certain"point"will"have"a"diminishing"effect"on"sales"price;"beyond"a" certain"size,"people"might"not"be"willing"to"pay"as"much"for"each"addiJonal"square"foot"of" living"space."This"results"in"what"is"called"a"“curvilinear"effect”,"in"which"case"addiJonal"terms" must"be"added"to"the"regression"model"to"capture"the"diminishing"returns"for"increasing" square"footage."A"linear"regression"model"will"predict"well"up"to"the"point"of"diminishing" returns."A^er"that"point,"the"model"will"sJll"be"predicJve"but"less"accurate"without"adjusJng" for"the"curvilinear"effect."As"indicated,"in"the"large"majority"of"circumstances"in"appraising,"the" linear"model"works"well"and"is"very"accurate.""
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Non4independence&of&Property&CharacterisDcs.&As"an"appraiser,"you"know"that"no"two" properJes"are"exactly"the"same"and"that"they"differ"from"each"other"in"mulJple"ways."It"makes" sense"then"that"in"esJmaJng"a"given"property’s"value,"you"consider"the"mulJple"ways"the" property"you"are"appraising"is"different"from"comparable"properJes."What"is"less"intuiJve"and" much"more"difficult"to"esJmate"on"your"own"is"the"degree"to"which"the"mulJple"property" characterisJcs"you"are"considering"are"themselves"associated"with"each"other"(i.e.,"nonP independent)"as"you"are"esJmaJng"their"associaJon"with"sales"price."That"is,"considered" alone,"the"number"of"bedrooms,"lot"size,"and"gross"living"area"might"each"account"for"some"of" the"difference"in"the"sold"prices"of"comparable"properJes.""However,"it"is"possible"that"number" of"bedrooms"is"not"completely"independent"of"gross"living"area"when"secng"a"price."Larger" properJes"could"tend"to"have"more"bedrooms"and"vice"versa."On"the"other"hand,"lot"size"could" very"well"be"largely"independent"of"both"gross"living"area"and"bedrooms."""
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