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{"sheet":"Testo_esercizio","index":0,"n_rows":3,"n_cols":6,"rows_kept":3,"cut":false,"hidden":false,"merged":[]}
[]
[null,null,null,null,null,"X = numero di dipendenti"]
[null,null,null,null,null,"Y=vendite in milioni di Euro"]

{"sheet":"Dati","index":1,"n_rows":388,"n_cols":15,"rows_kept":388,"cut":false,"hidden":false,"merged":[[71,3,72,7],[84,4,86,4],[84,5,86,5],[88,11,90,14],[76,11,77,12],[46,12,48,12],[66,11,66,13],[67,11,71,11],[82,12,85,12],[82,13,85,13],[46,13,48,13],[11,7,14,7],[43,12,44,12],[43,13,44,13],[23,3,23,6],[35,8,37,8],[35,9,37,9],[32,2,34,5]]}
[null,null,"X = numero di dipendenti",null,null,"Y=vendite in milioni di Euro"]
[]
[null,null,"xi","yi","xi^2","yi^2","xi*yi","Valori teorici","Residui ei","Residui al quadrato","(Valori teorici -media)^2","(Valori effettivi-media)^2","xiei","(xi-M(x))yi","(xi-M(x))^2"]
[null,"A",10,1.9,{"$f":"C4^2","v":100},{"$f":"D4^2","v":3.61},{"$f":"C4*D4","v":19},{"$f":"D$16+I$16*C4","v":1.8107142857142864},{"$f":"D4-H4","v":8.9285714285713524E-2},{"$f":"I4^2","v":7.971938775510069E-3},{"$f":"(H4-H$11/G$13)^2","v":1.41440051020408},{"$f":"(D4-D$11/G$13)^2","v":1.2100000000000002},{"$f":"C4*I4","v":0.89285714285713524},{"$f":"(C4-AVERAGE(C$4:C$10))*D4","v":-11.399999999999999},{"$f":"(C4-AVERAGE(C$4:C$10))^2","v":36}]
[null,"B",18,3.1,{"$f":"C5^2","v":324},{"$f":"D5^2","v":9.6100000000000012},{"$f":"C5*D5","v":55.800000000000004},3.3964285714285714,{"$f":"D5-H5","v":-0.29642857142857126},{"$f":"I5^2","v":8.7869897959183582E-2},{"$f":"(H5-H$11/G$13)^2","v":0.15715561224489791},{"$f":"(D5-D$11/G$13)^2","v":1.0000000000000018E-2},{"$f":"C5*I5","v":-5.3357142857142827},{"$f":"(C5-AVERAGE(C$4:C$10))*D5","v":6.2},{"$f":"(C5-AVERAGE(C$4:C$10))^2","v":4}]
[null,"C",20,3.2,400,10.240000000000002,64,3.7928571428571427,-0.59285714285714253,0.35147959183673433,0.62862244897959163,4.000000000000007E-2,-11.857142857142851,12.8,16]
[null,"D",8,1.5,64,2.25,12,1.414285714285715,8.5714285714284966E-2,7.3469387755100753E-3,2.5144897959183652,2.25,0.68571428571427973,-12,64]
[null,"E",30,6.2,900,38.440000000000005,186,5.7749999999999995,0.42500000000000071,0.18062500000000059,7.7006249999999969,10.240000000000002,12.750000000000021,86.8,196]
[null,"F",12,2.8,144,7.839999999999999,33.599999999999994,2.2071428571428573,0.59285714285714253,0.35147959183673433,0.62862244897959163,4.000000000000007E-2,7.1142857142857103,-11.2,16]
[null,"G",14,2.2999999999999998,196,5.2899999999999991,32.199999999999996,2.6035714285714286,-0.30357142857142883,9.2155612244898114E-2,0.15715561224489791,0.49000000000000027,-4.2500000000000036,-4.5999999999999996,4]
[null,"Tot.",{"$f":"SUM(C4:C10)","v":112},21,2128,77.28,402.59999999999997,21,-8.8817841970012523E-16,1.078928571428571,13.201071428571421,14.280000000000003,{"$f":"SUM(M4:M10)","v":1.0658141036401503E-14},{"$f":"SUM(N4:N10)","v":66.600000000000009},{"$f":"SUM(O4:O10)","v":336}]
[null,null,null,null,null,null,null,"Oss: i valori teorici sono interpretabili come le medie delle variabili casuali Y_1,…, Y_7 che hanno generato i dati osservati riportati nella zona D4:D10"]
[null,null,null,null,null,"n=",7]
[]
[]
[null,null,"a=",{"$f":"(D11*E11-C11*G11)/(G13*E11-C11^2)","v":-0.17142857142857018},null,null,null,"b=",{"$f":"(G13*G11-C11*D11)/(G13*E11-C11^2)","v":0.19821428571428565}]
[]
[]
[]
[null,null,null,null,"s=",{"$f":"SQRT(J11/(G13-2))","v":0.46452740961725197},null,null,"s(b)=",{"$f":"F20/SQRT(O11)","v":2.5342047820866843E-2},null,null,"s(a)=",{"$f":"F20*SQRT(1/G13+AVERAGE(C4:C10)^2/O11)","v":0.44185370189413475}]
[]
[null,null,null,null,null,{"$f":"STEYX(D4:D10,C4:C10)","v":0.4645274096172517}]
[]
[null,null,null,"Modello di regressione tramite la funzione REGR.LIN",null,null,null,null,"t(b)=",{"$f":"I16/J20","v":7.8215575598067666},null,null,"t(a)=",{"$f":"D16/N20","v":-0.38797586326354538}]
[null,null,null,null,{"$f":"LINEST(D4:D10,C4:C10,TRUE,TRUE)","v":0.1982142857142857},-0.17142857142857126]
[null,null,null,null,2.5342047820866836E-2,0.44185370189413475]
[null,null,null,null,0.92444477791116453,0.46452740961725203,null,null,"p value =",{"$f":"TDIST(J24,$G13-2,2)","v":5.4781485414803256E-4},"==> rifiuto decisamente H0:beta=0",null,"p value =",{"$f":"TDIST(ABS(N24),$G13-2,2)","v":0.71400191054341966},"==>accetto l'ipotesi H0:alpha=0"]
[null,null,null,null,61.176762661370432,5]
[null,null,null,null,13.201071428571431,1.0789285714285712]
[]
[]
[null,null,null,null,null,null,null,null,"t0.025(5)"]
[null,null,"Modello di regressione tramite il componente aggiuntivo di Excel Analisi dei dati",null,null,null,null,null,"t0.975(5)",{"$f":"TINV(0.05,5)","v":2.570581835636315},null,null,"Estremo inf. intervallo confidenza di α","Estremo sup. intervallo confidenza di α"]
[null,null,null,null,null,null,null,null,null,null,null,"α",{"$f":"D16-N20*J33","v":-1.3072496715262962},{"$f":"D16+N20*J33","v":0.96439252866915592}]
[]
[null,null,"OUTPUT RIEPILOGO",null,null,null,null,null,"Estremo inf. intervallo confidenza","Estremo sup. intervallo confidenza"]
[null,null,null,null,null,null,null,"β"]
[null,null,"Statistica della regressione"]
[null,null,"R multiplo",0.96148051353689146,null,null,null,null,{"$f":"I16-J33*J20","v":0.13307047790813847},{"$f":"I16+J33*J20","v":0.26335809352043282}]
[null,null,"R al quadrato",0.92444477791116453]
[null,null,"R al quadrato corretto",0.90933373349339741,null,{"$f":"FDIST(G47,D47,D48)","v":5.4781485414803213E-4}]
[null,null,"Errore standard",0.46452740961725203,null,null,null,null,null,null,null,null,2.5000000000000001E-2,0.97499999999999998]
[null,null,"Osservazioni",7]
[null,null,null,null,null,null,null,null,null,null,null,null,"Quantile 0.975 di una v.a. Chi quadrato con n-2 gradi di libertà","Quantile 0.025 di una v.a. Chi quadrato con n-2 gradi di libertà"]
[null,null,"ANALISI VARIANZA"]
[null,null,null,"gdl","SQ","MQ","F","Significatività F",null,null,null,null,{"$f":"CHIINV(M42,$G13-2)","v":12.832501994030029},{"$f":"CHIINV(N42,$G13-2)","v":0.83121161348666384}]
[null,null,"Regressione",1,13.201071428571431,13.201071428571431,61.176762661370432,5.4781485409422274E-4,null,null,null,null,"Estremo inf. intervallo confidenza di σ^2","Estremo sup. intervallo confidenza di σ^2"]
[null,null,"Residuo",5,1.0789285714285712,0.21578571428571425,null,null,null,null,null,"σ^2"]
[null,null,"Totale",6,14.28]
[null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"$J11/M46","v":8.4077802748872596E-2},{"$f":"$J11/N46","v":1.2980191252415432}]
[null,null,null,"Coefficienti","Errore standard","Stat t","Valore di significatività","Inferiore 95%","Superiore 95%"]
[null,null,"Intercetta",-0.17142857142857126,0.44185370189413486,-0.38797586326354777,0.71400191056669371,-1.3072496711114965,0.96439252825435395]
[null,null,"Variabile X 1",0.1982142857142857,2.5342047820866843E-2,7.8215575598067684,5.4781485409422339E-4,0.133070477931929,0.26335809349664241]
[]
[]
[]
[null,null,"OUTPUT RESIDUI"]
[]
[null,null,"Osservazione","Y prevista","Residui"]
[null,null,1,1.8107142857142857,8.9285714285714191E-2]
[null,null,2,3.3964285714285714,-0.29642857142857126]
[null,null,3,3.7928571428571427,-0.59285714285714253]
[null,null,4,1.4142857142857144,8.5714285714285632E-2]
[null,null,5,5.7750000000000004,0.42499999999999999]
[null,null,6,2.2071428571428573,0.59285714285714253]
[null,null,7,2.6035714285714286,-0.30357142857142883]
[null,null,null,null,null,null,null,null,null,null,null,"3 diversi modi per calcolare un valore previsto dato x0"]
[null,null,null,null,null,null,null,null,null,null,null,"y_0 previsto (ossia vendite previste in corrispondenza di un numero di dipendenti pari a 16)",{"$f":"D16+I16*16","v":3},"Utilizzando i parametri stimati"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"TREND(D4:D10,C4:C10,16,TRUE)","v":3},"Utilizzando la funzione \"Tendenza\""]
[null,null,null,"VERIFICA DELL'IPOTESI NULLA H0:β=0.25"]
[null,null,null,"Notiamo preliminarmente che il valore 0.25 è compreso nell'intervallo al 95%. Ci attendiamo quindi che il risultato del test non risulti significativo al livello di significatività del 5%",null,null,null,null,null,null,null,null,{"$f":"FORECAST(16,D4:D10,C4:C10)","v":3},"Utilizzando la funzione \"Previsione\""]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Varianza errore di previsione="]
[null,null,null,"Test t=",null,{"$f":"(I16-0.25)/J20","v":-2.0434699931026721}]
[]
[null,null,null,"pvalue del risultato del test",null,{"$f":"TDIST(ABS(F75),5,2)","v":9.6441521266136129E-2},null,null,null,null,null,"radice quadrata della varianza dell'errore di previsione sqrt((var(e_0))"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"F20*SQRT(1+1/G13+(16-AVERAGE(C4:C10))^2/O11)","v":0.49660068958667297}]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Estremo inf. intervallo confidenza","Estremo sup. intervallo confidenza"]
[]
[null,null,null,null,"Funz. di densità della T con 5 gradi di libertà nell'intervallo [-3 3]","Funz. di ripartizione della T con 5 gradi di libertà nell'intervallo [-3 3]"]
[null,null,null,null,null,null,null,"gradi di libertà=",5]
[null,null,null,"x",null,null,null,null,null,null,null,null,{"$f":"M68-J33*N78","v":1.7234472877840303},{"$f":"M68+J33*N78","v":4.2765527122159694}]
[null,null,null,-3,{"$f":"_xlfn.T.DIST(D88,gdl,FALSE)","v":1.7292578800222964E-2},{"$f":"_xlfn.T.DIST(D88,gdl,TRUE)","v":1.5049623948731293E-2}]
[null,null,null,-2.98,1.7743444218716348E-2,1.5399963417372839E-2,null,null,null,null,null,"Commento: c'è una probabilità pari a 0.95 che le vendite si collochino nell'intervallo 1.72 milioni di euro, 4.28 milioni di Euro quando il numero di dipendenti è pari a 16"]
[null,null,null,-2.96,1.8206944965104287E-2,1.5759445950841007E-2]
[null,null,null,-2.94,1.8683444027689712E-2,1.6128327869212859E-2]
[null,null,null,-2.92,1.9173314319417132E-2,1.6506872851223459E-2]
[null,null,null,-2.9,1.9676938890598517E-2,1.689535213488591E-2]
[null,null,null,-2.88,2.0194711141441404E-2,1.7294044722364704E-2]
[null,null,null,-2.86,2.0727035033933729E-2,1.7703237589093958E-2]
[null,null,null,-2.84,2.1274325302601642E-2,1.8123225897122806E-2]
[null,null,null,-2.82,2.1837007663615671E-2,1.8554313212660583E-2]
[null,null,null,-2.8,2.2415519021677269E-2,1.8996811727782628E-2]
[null,null,null,-2.78,2.3010307674072548E-2,1.9451042486246871E-2,null,null,null,null,null,"Dati di input per rappresentare graficamente l'intervallo di confidenza"]
[null,null,null,-2.76,2.3621833511231809E-2,1.9917335613357279E-2,null,null,null,null,null,"x0",16]
[null,null,null,-2.74,2.4250568213082378E-2,2.0396030549798164E-2,null,null,null,null,null,"y cappello_0",{"$f":"M68","v":3}]
[null,null,null,-2.72,2.4896995440429746E-2,2.0887476289346708E-2]
[null,null,null,-2.7,2.5561611020544554E-2,2.1392031620356841E-2,null,null,null,null,null,"Err. superiore",{"$f":"N87-M101","v":1.2765527122159694}]
[null,null,null,-2.68,2.6244923126075383E-2,2.1910065370889551E-2,null,null,null,null,null,"Err. inferiore",{"$f":"M101-M87","v":1.2765527122159697}]
[null,null,null,-2.66,2.6947452446344243E-2,2.2441956657346888E-2]
[null,null,null,-2.64,2.7669732350017285E-2,2.2988095136447451E-2]
[null,null,null,-2.62,2.8412309038075585E-2,2.3548881260359981E-2]
[null,null,null,-2.6,2.9175741685939279E-2,2.4124726534790041E-2]
[null,null,null,-2.58,2.9960602573524796E-2,2.4716053779790581E-2]
[null,null,null,-2.56,3.0767477201937662E-2,2.5323297393042097E-2]
[null,null,null,-2.54,3.1596964395423068E-2,2.59469036153217E-2]
[null,null,null,-2.52,3.2449676387113088E-2,2.6587330797851663E-2]
[null,null,null,-2.5,3.3326238887022831E-2,2.7245049671188116E-2]
[null,null,null,-2.48,3.4227291130658741E-2,2.7920543615278362E-2]
[null,null,null,-2.46,3.5153485906509623E-2,2.8614308930282446E-2]
[null,null,null,-2.44,3.6105489560595658E-2,2.9326855107718021E-2]
[null,null,null,-2.42,3.7083981976153188E-2,3.0058705101450884E-2]
[null,null,null,-2.4,3.8089656526431967E-2,3.0810395598013931E-2]
[null,null,null,-2.38,3.9123219998479064E-2,3.1582477285695416E-2]
[null,null,null,-2.36,4.018539248567856E-2,3.2375515121794228E-2]
[null,null,null,-2.34,4.1276907246708967E-2,3.3190088597394148E-2]
[null,null,null,-2.3199999999999998,4.239851052847253E-2,3.4026791998961352E-2]
[null,null,null,-2.2999999999999998,4.355096135044003E-2,3.4886234666018645E-2]
[null,null,null,-2.2799999999999998,4.473503124774459E-2,3.5769041244098916E-2]
[null,null,null,-2.2599999999999998,4.5951503970247901E-2,3.6675851932124692E-2]
[null,null,null,-2.2400000000000002,4.7201175134690139E-2,3.7607322723304963E-2]
[null,null,null,-2.2200000000000002,4.8484851826926682E-2,3.8564125638580936E-2]
[null,null,null,-2.2000000000000002,4.9803352151145085E-2,3.9546948951591186E-2]
[null,null,null,-2.1800000000000002,5.1157504722850411E-2,4.0556497404065042E-2]
[null,null,null,-2.16,5.2548148102302919E-2,4.159349241048501E-2]
[null,null,null,-2.14,5.3976130164994196E-2,4.2658672250794838E-2]
[null,null,null,-2.12,5.5442307405651141E-2,4.3752792249857453E-2]
[null,null,null,-2.1,5.6947544172170565E-2,4.4876624942299347E-2]
[null,null,null,-2.08,5.8492711825804122E-2,4.6030960221301556E-2]
[null,null,null,-2.06,6.0078687823840959E-2,4.7216605469825854E-2]
[null,null,null,-2.04,6.1706354720970677E-2,4.8434385672688263E-2]
[null,null,null,-2.02,6.3376599085457633E-2,4.9685143507813403E-2,null,{"$f":"\"Pr (T<\" & F75 &\")=\" & _xlfn.T.DIST(F75,5,TRUE)","v":"Pr (T<-2,04346999310267)=0,0482207606330681"}]
[null,null,null,-2,6.5090310326216497E-2,5.0969739414929181E-2]
[null,null,null,-1.98,6.6848379426854163E-2,5.228905163987816E-2]
[null,null,null,-1.96,6.8651697582732332E-2,5.3643976252647073E-2]
[null,null,null,-1.94,7.0501154737114297E-2,5.5035427137134794E-2]
[null,null,null,-1.92,7.2397638012486498E-2,5.6464335950601484E-2]
[null,null,null,-1.9,7.4342030033196185E-2,5.793165205066407E-2]
[null,null,null,-1.88,7.6335207135619157E-2,5.9438342387625215E-2]
[null,null,null,-1.86,7.8378037462173838E-2,6.0985391359850864E-2]
[null,null,null,-1.84,8.0471378935625851E-2,6.2573800629836668E-2]
[null,null,null,-1.82,8.2616077110286276E-2,6.4204588898534642E-2]
[null,null,null,-1.8,8.4812962896903751E-2,6.5878791635446077E-2]
[null,null,null,-1.78,8.7062850158276889E-2,6.7597460761924327E-2]
[null,null,null,-1.76,8.9366533172884524E-2,6.9361664285074023E-2]
[null,null,null,-1.74,9.1724783964140577E-2,7.1172485879583122E-2]
[null,null,null,-1.72,{"$f":"_xlfn.T.DIST(D152,gdl,FALSE)","v":9.4138349493233561E-2},{"$f":"_xlfn.T.DIST(D152,gdl,TRUE)","v":7.3031024414778795E-2}]
[null,null,null,-1.7,9.6607948713911859E-2,7.4938393424161961E-2]
[null,null,null,-1.68,9.9134269488024923E-2,7.6895720514646979E-2]
[null,null,null,-1.66,0.10171796536113153,7.8904146712712703E-2]
[null,null,null,-1.64,0.10435965219804023,8.0964825744666027E-2]
[null,null,null,-1.62,0.10705990467875781,8.3078923248217626E-2]
[null,null,null,-1.6,0.10981925265599095,8.5247615912590918E-2]
[null,null,null,-1.58,0.11263817737607228,8.7472090544410436E-2]
[null,null,null,-1.56,0.11551710756597332,8.9753543056665469E-2]
[null,null,null,-1.54,0.11845641538991698,9.2093177378102575E-2]
[null,null,null,-1.52,0.12145641228001788,9.4492204280482939E-2]
[null,null,null,-1.5,0.12451734464635514,9.6951840121236754E-2]
[null,null,null,-1.48,0.12763938947292541,9.9473305499166373E-2]
[null,null,null,-1.46,0.13082264980702593,0.10205782382098944]
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