ࡱ> HJKABCRoot EntryRoot Entry_ 'I@ContentsPEmbedding 1 Fb '_ 'WorkbookD{  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFG@MNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~CompObj fSummaryInformation(DocumentSummaryInformation8|OlePres000L<Ole ""X@t飸 Model K1:Co ModelconRegress HeadeRegressi CustoRegress HeadeRegressRegressMixeRegressStanSheetDaCou UserDCouRegress333333?Regressi333333?Regressi?Regression?Mode Model Model Model Model Model Model Model Model Model ModelTeRegressRegressiRegress_1RegressRegress Sheet UserD UserD RegressRegressionContourPlotOpOffering Price PredictorEIEChart Data Offering Price Predi Price ($)_1333333?333333???real estate data!Offering Price PredictorCountySchool District #Bathrooms #Bedrooms Price ($)FRAColumbus?@FRAUpper Arlington?@FRAColumbus?@FRAColumbus@@FRAColumbus?@FRAHilliard@@FRA Plain Local@@LIC Reynoldsburg@@FRAColumbus?@FRAHilliard@@FRA Westerville@@FRAHilliard@@LIC Reynoldsburg@@FRABexley?@FRAHilliard@@FRA Westerville@@FRAColumbus@@FRAColumbus@@FRAHilliard@@DEL Olentangy@@FRA Westerville@@FRAHilliard@@FRA Plain Local@@DEL Olentangy@@FRA Worthington@@FRA Westerville@@LIC Reynoldsburg@@FRAColumbus@@FRAHilliard@@LIC Reynoldsburg@@FRAUpper Arlington@@FRAGahanna@@LIC Reynoldsburg@@FRAHilliard@@DEL Westerville@@FRAColumbus@@LIC Reynoldsburg@@FRA Westerville@@FRA Plain Local@@FRABexley?@DEL Olentangy@@DEL Westerville@@FRAColumbus@@FRAGahanna@@FRAColumbus@@FRAHilliard@@FRAColumbus@@FRABexley?@FRA Westerville@@DEL Westerville@@FRADublin@@FRADublin@@FRAColumbus?@FRAHilliard@@FRAHilliard@@DEL Olentangy@@FRAColumbus?@DEL Olentangy@@FRAColumbus@@FRAColumbus@@FRADublin@@FRA Plain Local@@DEL Olentangy@@DEL Olentangy?@FRAColumbus?@FRAHilliard@@FRA Plain Local@@FRADublin@@FRAGahanna@@FRA Westerville@@DEL Westerville@@FRABexley@@FRAColumbus@@FRAGahanna@@LIC Reynoldsburg@@FRA Westerville@@FRA Plain Local@@FRADublin@@FRAColumbus?@FRAColumbus@@FRAColumbus?@FRAColumbus@@FRAHilliard@@FRAColumbus?@FRADublin@@DEL Olentangy@@FRAUpper Arlington@@FRA Plain Local@@LIC Reynoldsburg@@FRAHilliard@@DEL Olentangy@@FRADublin@@FRADublin@@FRAHilliard@@FRAColumbus@@FRAColumbus?@FRADublin@@DEL Olentangy@@FRA Reynoldsburg@@LIC Reynoldsburg@@FRA Reynoldsburg@@FRADublin@@FRAUpper Arlington?@FRAHilliard@@FRABexley@@FRADublin@@FRAColumbus@@FRAGahanna@@FRA Plain Local@@DEL Olentangy@@FRAHilliard@@DEL Olentangy@@FRABexley@@FRAColumbus@@DEL Westerville @@FRAColumbus @@FRADublin@@FRAUpper Arlington@@DEL Olentangy@@DEL Olentangy@@FRADublin@@DEL Olentangy@@FRAHilliard@@FRAColumbus?@FRADublin@@FRADublin@@FRAHilliard@@FRAGahanna@@FRA Reynoldsburg@@FRAUpper Arlington?@FRAHilliard@@FRA Westerville@@DEL Olentangy@@FRAColumbus?@FRAHilliard@@FRA Worthington@@FRA Plain Local@@DEL Olentangy @@FRA Westerville@@DEL Westerville@@DEL Westerville@@DEL Olentangy@@DEL Westerville@@FRADublin @@FRA Plain Local@@DEL Westerville@@FRA Worthington @@FRAColumbus@@FRAHilliard@@FRA Plain Local?@FRAUpper Arlington@@FRA Worthington@@DEL Olentangy@@FRAColumbus@@DELDublin@@DEL Olentangy@@FRAHilliard@@FRAGahanna@@FRAGahanna@@FRAColumbus@@DEL Olentangy@@FRAGahanna@@DEL Olentangy@@DELDublin@@FRA Worthington@@FRADublin @@DEL Westerville@@FRADublin @@DEL Olentangy@@DELDublin @@FRAUpper Arlington@@DEL Westerville@@FRAUpper Arlington@@FRAColumbus@@FRA Plain Local@@FRAColumbus@@FRAHilliard@@DEL Westerville@@DEL Olentangy@@FRAColumbus @@FRAUpper Arlington@@FRAGahanna@@FRADublin@@DEL Olentangy @@FRAUpper Arlington @@FRADublin @@FRADublin @@FRAColumbus@@DEL Westerville@@FRA Plain Local@@FRABexley @@FRAUpper Arlington@@FRA Worthington@@FRADublin@@DELDublin@@FRABexley@@FRAHilliard@@FRADublin@@FRAUpper Arlington@@FRAUpper Arlington@@FRABexley @@FRADublin@@FRA Worthington @@FRAGahanna@@FRABexley@@FRAUpper Arlington@@FRABexley@@DEL Olentangy@@DEL Westerville@@DEL Olentangy@@DEL Olentangy @@FRADublin@@FRA Worthington@@FRAUpper Arlington@@DEL Olentangy@@FRADublin @@FRA Plain Local @@DEL Westerville @@FRABexley @@DEL Olentangy @@FRAUpper Arlington@@FRAUpper Arlington@@DEL Westerville @@FRA Worthington @@FRA Plain Local@@FRA Plain Local @@CountySchool District #Bathrooms #Bedrooms const K1:CountyK2:School District X1:#Bathrooms X2:#BedroomsX1X2 K1*X2 X1*X2 X1X2OAA 'A~AAAA@=A~A A`AYAYAAAA`4A@A`AA@A`.A`.A`.A`.AAAAAAA`(A`(AGAcAfAfAfAA  A  A`" A` A` A` A` A` A; 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The regression model predictions might alsoMhelp home builders decide on the number of bathrooms and bedrooms appropriate+for each location to maximize sale profits.Data description Input factors Response(s)CommentsAcknowledgementswww.realestatewarehouse.comYThese are based on real estate offering prices as of 7/8/2003 in the Columbus, Ohio area.PCollecting more data and considering more factors that could affect the offering/prices should help the results of the analysis.DThis data and compiled by Sagata Ltd. based on the information from 9County. Greater Columbus, Ohio resides in three counties.GSchool District. Generally corresponds (highly correlates) to the city.=Bath. Descrip. Verbal description of the number of bathrooms.F#Bathrooms. Number of bathrooms, counting half baths as 0.5 bathrooms #Bedrooms. Number of bedrooms. Price ($). Asking price. 6City. Municipality that is a suburb of Columbus, Ohio.* so that 2 half baths make one bathroom.Output for Price ($)Regression EquationPrice ($) = - 31975.9 - 70479.9*County_LIC + 130250*County_DEL + 72267.1*School District_Upper Arlington - 26341.5*School District_Hilliard + 37069*School District_Plain Local + 2835.38*School District_Reynoldsburg - 42949.9*School District_Westerville + 47403.4*School District_Bexley - 44237.2*School District_Olentangy + 56691*School District_Worthington + 2772.11*School District_Gahanna - 2117.31*School District_Dublin - 184695*#Bathrooms + 249868*#Bedrooms + 70429.3*#Bathrooms - 63674.8*#Bedrooms + 868.06*County_LIC*#Bedrooms - 19406.7*County_DEL*#Bedrooms + 25363.2*#Bathrooms*#Bedrooms - 9076.62*#Bathrooms + 3824.79*#Bedrooms Summary Statistics CriterionValueR^2R^2 adj R^2 predictR^1PRESS s (est. err.)SSE(LSE)/SSE(LAD)LAD: R^1 M-Fair: R*; Note: LAD:R is not provided for other than the LAD metric.? Note: Mfair:R is not provided for other than the Mfair metric.ANOVAdfSSMSFp-value Regression ResidualsTotalCoefficient Estimates CoefficientsStandard Errort Stat Lower 95% Upper 95%VIFconst County_LIC County_DELSchool District_Upper ArlingtonSchool District_HilliardSchool District_Plain LocalSchool District_ReynoldsburgSchool District_WestervilleSchool District_BexleySchool District_OlentangySchool District_WorthingtonSchool District_GahannaSchool District_Dublin #Bathrooms #BedroomsCounty_LIC*#BedroomsCounty_DEL*#Bedrooms#Bathrooms*#Bedrooms #Bathrooms #BedroomsTerm SignificancetermSSR_diff021011(0)County*#Bedrooms3D Plot Engine (for Price ($))VariableLowHighFixed Plot RoleX AxisY Axis!Prediction Engine (for Price ($)) PredictionError Normal ScoresLevels Predictionsk1:FRAk1:LICk1:DELk2:Columbus k2:Upper_Arlingtonk2:Hilliard k2:Plain_Local k2:Reynoldsburg k2:Westerville k2:Bexley k2:Olentangy k2:Worthington k2:Gahanna k2:Dublin #Bathrooms:1 #Bathrooms:3.5#Bathrooms:6 #Bedrooms:2 #Bedrooms:4 #Bedrooms:6Response Yjq  .?   $ l}  >O  @  dMbP?_*+%M6\\OFFICE\HP OfficeJet G85XC od,,LetterDINU"4$ $$$$"d,,??U} I }  } I }  k      - !. / 0 !1 #2 #3 4$A֊? 5$? 6 $?  7 $~\ ?  8 ZŷqB  9 % B"@  : $f9?  ; = > < = ? !@ #0 #A #B #C #D #E  F~ 5@CNiB#B%08 @&S2TU<  G~ i@)P^?mB},YA H~  l@>V){B !I #0 #J #K #L #E #M #N #O %P%X9%~A% $,!~o)?%Q +:"%zF A %0 %Q%$4%}ߓA%\mmٿ$?!?%2>M%J< A%leK@ %R%*K@%Q/@%և?$FUPȶ?%i%v7M*A% 4d\T@ %S%=c=㱤@%NGǮ@%1$R @$a;K,I?%^Q-Q@%"r\@% g? %T%D^%E鬊@%$qlB?%.<%X.k@%?8 &&2&26666666>>&brRB&p !"#$%&'()*+,-./03456789:;<=>? %U %W@ %`J@ %f? $`n̓? %8`̹ %Nd@ %aE? !%V!%RO&@!%4^q @!%:?!$| JQ?!%O!%k1]@!%! @ "%W"% k"%~@"%- 9"$OflG?"%(4"%R@"%-&@ #%X#%&k%@#%s,@#%)[p?#$1Z?#%2æKd#%8y/@#%ٝpݷz? $%Y$%)$%:r@$%LI$$M?$%]$%V@$%A) @ %%Z%%Eko`@%% R@%%>T@%$Þť?%%@A4s&@%%d=5@%%=ͦ? &%[&%,7@&%˝U@&%΍?&$<->?&%,H&%e瞀3@&%u[oA? '%\'%S'%9D@'%n;ۻ'$;?'%;'%89{@'%ڥ? (%(%`?(% _,@(%q($o:1I?(%x(% Q/@(%PVf@ )%)%8٨__A)%!QS A)%4ٻ?)$<?)%0^ a)%kRr%A)%ޱƐ@ *%]*%1O1@*%߷@*%~NFCK@*$Yf˗?*%8i/@*%A*%Uӄ@ +%^+%NxZ+%F[U@+%l@+$c?+%};+%#@+%nƕ`@ ,%_,%،p @,%ɡm@,%@1m?,$(X?,%MvV,%X@,%,5xHI@ -%`-%ɨ-%&'@-%1h-$Cg?-%Z-%U @-%pS@ .%a.%@.%Jrx@.%Feۨ?.$Xp,?.%xbsҾ.%o8&@.%WBg@ /%b/% HWO/%cJ(= @/%>/$P |?/%D.歑/%@ Ë/%Fh@ 0%c0%g@0% K{/ @0%0?0$~:?0%"90%b8@0%eV@ 3!d3 4#e 4#A 4#f 4#D 4#E 4 5'P 5(g 5= 5= 5$= 5 6' 6(h6U^ғB6$#h@?6$B"? 6 7' 7(i7ǥEB7%T2@7$p H1? 7 8' 8(j8 fB8%;9[ڛ @8$m1I? 8 9' 9'k~ 9 9=~ 9$? 9 :'] :(j:vcB:%1e@:$Wf˗? : ;'^ ;(j;;& A;%?;$`? ; <'l <(h<A<$LN3?<$Έ~? < ='a =(j==Q-B=%f@=$p,? = >'b >(j>m? B>%N@>$] |? > ?'c ?(j?hXnhA?$r+5??$ى:? ?@>D&VVbbbVbbbbbBCDEFG B!mB C#n C#o C#p C/q C/r D, D)) D0 D0q E- E E0 E0q F-F?@0 @ F0s G.G"@"@0@ G0td F888bcdefghij b2u b" cvc*A c dwd+aD@ d e#n e#o e#p e/q f f f0 g g g0 hh?@0? ii@@3@j)))) ..8****h65P(  ~  <r XPP? ]4@r  M H۵I\1 a8<bIn brief: Regression Equation shows your fitted model for visual inspection. More: (Sagata Regression Pro). The model might contain extra "indicator" variables that were automatically introduced to treat categorical factors. Beware: Avoid reading the coefficients off of this equation. Refer to the Coefficient Estimates table for more precise values.<82 JM(S56aid~~  <,s XPP?x]4@,sT  ]Q5Hf/e  #<$In brief: Summary Statistics table.<2 y#~~  <s XPP?]4@sD  @us3H$'  \8<]In brief: R^2 (R_squared) indicates how close the match is between predictions from your fitted model and observed responses. 0 <= R^2 <= 1. R^2 values close to 1 indicate good match. More: Whether the "match" mentioned above is close or not should be decided relative to something. Typically, your model is benchmarked against a primitive model that includes only a constant (often called "intercept"). R^2=1-SSE/SST (see ANOVA table output for brief help on SSE and SST) However, if your model does not include a constant, then this software benchmarks your model against a zero constant. R^2=1-SSE/SST(0) Beware: R^2 value close to 1 do not always mean a good model. Sometimes it is due to overfitting, i.e. having too many parameters in the model that make it possible to fit the data very well. Prediction properties might be very poor for such models.<82 o(2b5j\o) ~~  <s XPP?]4@s  iyy)MA2:  L(<MIn brief: R^2-adjusted has an interpretation similar to R^2. It tries to remedy some faults of R^2 by not being so high when the model has many terms and is possibly bad. More: Similarly to R^2 a benchmark is chosen to be a model with only a constant (when your model includes a constant) R^2-adjusted=1 - [SSE/(n-p)] / [SST/(n-1)]<(2 (Ldh~~  <Xt XPP?]4@Xt  uCM5]R%  (<In brief: The R-squared of prediction measures the model's ability to predict. Its values are between 0 (bad prediction) and 1 (best prediction). This statistic might be preferred to the regular R^2. More: This statistic differs from R^2 in replacing the actual SSE by the predicted SSE (PRESS). Therefore, like PRESS, R-squared of prediction uses a basic cross-validation of the model's ability to predict by removing one data point at a time.<(2 (zd ~~  <t XPP? ]4@t  .K\Il|%  (<In brief: The (LSE-based) R^1 is the regular R^2 rescaled to be in the same scale (instead of being a square) as the responses. It is also between 0 and 1. More: See formulas and references in Sagata Help.<(2 (ool~~  < u XPP? ]4@ u  &p"MEl\8  (<In brief: PRESS - predicted residual sum of squares. PRESS addresses both model fit and model prediction properties. PRESS is always >=0. Smaller PRESS is better. Its range is not standardized and depends on specific data. More: PRESS=SUM (y_i - y'_(i) )^2, sum is over i=1,...,number of observations. y_i - is the actual observation at point i y'_(i) is obtained as the result of the following steps: 1. Remove i-th observation from the data 2. Fit the model to the reduced data 3. Use this model to predict at the removed i-th point. This prediction is y'_(i) Using this definition results in slow computation. Refer to the standard literature for the formula that uses the "hat" matrix.<(2 &(t n:~~  <u XPP? ]4@u  ៟BJ7uk  8<In brief: s (estimated error) is an empirical estimate of the repeatability errors in your observations at any point. More: s=sqrt(MSE)=sqrt( SSE/dfE ), where dfE is error degrees of freedom (see comments for ANOVA table or accompanying Help). Under the standard idealistic assumptions, this estimate is an unbiased estimate of the standard deviation of the errors. Beware: Most statistics (and s-estimate is one of them) are calculated based on idealistic assumptions about your data origins. For example, if the regression model is not the same as the true model of your system, then the missed/misrepresented terms will be added to the error estimate.<82 v(|o5wU ou~~   <u XPP? i]4 @u _S:0Fyr7?  =(<>In brief: The ratio SSE(LSE)/SSE(LAD) can be used as an indicator of outliers. Its values are between 0 ("bad") and 1 ("good"). The values below 0.7 might indicate the presence of influential outliers. More: The ratio of the sum of squared errors (SSE) of the model derived from LSE fitting to the SSE of the model derived from LAD fitting will be close to 1 when both metrics result in similar models. However, if there are influential outliers in the data, then LSE-based model will respond to them more drastically and the SSE(LSE)/SSE(LAD) ratio is likely to decrease.<(2 (= n:~~   <Lv XPP? ]4 @LvT !ԆK3`  t(<uIn brief: The R^1 for LAD metric is analogous to the regular R^2, but in the context of the LAD metric. Its values are also between 0 (bad fit) and 1 (best fit). More: LAD: R^1 has a potential benefit of being more interpretable since it's in the same scale as the response. LAD:R^1 might be compared with R^1 (for LSE) value. See Sagata Help for formulas and references.<(2 (tma(~~   <v XPP?]4 @vD P8JV'6$  z(<{In brief: The R for M-fair statistic is analogous to the regular R^2, but in the context of the M-fair metric. Its values are also between 0 (bad fit) and 1 (best fit). More: Because of the nature of M-fair metric, Mfair:R is not in the same scale as the response. Mfair:R should not be compared with LAD:R^1 nor LSE:R^1 statistics. See Sagata Help for formulas and references.<(2 (zsda~~   <w XPP? Z]4 @w C`)Ai5FA  <In brief: ANOVA Table shows how much of your data variation is explained by the model you selected. Also, it provides a statistical test to evaluate your model.<2 a~~   <xw XPP?@i]4 @xw N< LNG^  (<In brief: df - degrees of freedom. Regression df = number of model terms (usually -1) Residual df = Total df - Regression df Total df = number of observations (usually -1) More: Degrees of freedom are used to standardize some quantities. For example, SSE/df(Residual) gives an estimate of squared errors of observations. If the model includes a constant, then a 1 is subtracted in the formulas above. Otherwise, 1 is not subtracted.<(2 J(ota~~  <w XPP? $Z]4@w Sk&VQ@D{`  a(<bIn brief: SSR (Sum of Squares of Regression) shows how much of the data variation is explained by your regression model. SSE (Sum of Squares of Error (Residuals) ) shows the variation unexplained by your regression model. SST (Total Sum of Squares) is the total variation in the original data. More: The following equality is true for least squares regression SST=SSR + SSE (or WSST=WSSR+WSSE in case you are using weighted data in Sagata Regression Pro), where SST=SUM (y_i - m)^2, SSR=SUM (y'_i - m)^2, SSE=SUM (y_i - y'_i )^2, over i=1, ... , number of observations, where y_i - original observations of the response, y'_i - predicted observations of the response at the observation points using your fitted model, m is equal to the average of the observed responses or 0 depending on whether the model includes a constant or not, respectively.<(2 ((. aos ~~  <@x XPP? 0]4@@x K G^RK   (< In brief: MS - mean squares of (Regression and Error (Residuals)). It is obtained from corresponding SS by dividing by its df. More: MSR = SSR / df(Regression), MSE = SSE / df(Residual). MSE has the meaning of an estimate of the variance of the observation error.<(2 <( o o~~  <x XPP? ]4@x /.CkHFf  (<In brief: F-statistic. It is the ratio of MSR to MSE. High values imply that your model is useful. See also p-value. Beware: Most statistics (and F-statistic is one of them) are calculated based on idealistic assumptions about your data origins.<(2 u5}@ool~~  <y XPP?U ]4@y Nz+}  _8<`In brief: p-value < threshold (commonly, 0.05 is used for the threshold) indicates the usefulness of your regression model. More: p-value for ANOVA is the probability that such high or higher an F value as you observed for your model will be observed for a model with only a constant present (or no constant if your model does not include one) and other terms set to zero. So, the smaller the p-value the more useful your model is. Beware: Most statistics (and p-value is one of them) are calculated based on idealistic assumptions about your data origins. These assumptions almost never hold in practice.<82 1|(5+_ohe~~  <ly XPP?si]4@lyT C%8GuQ3c  @(<AIn brief: Information in this row relates to the regression model. More: For least squares regression, SST=SSR + SSE SST - total sum of squares SSR - regression sum of squares SSE - regression sum of squares (or sum of squares of error). The Regression row of the ANOVA table deals with the quantities derived from SSR.<(2 C(I@ldn~~  <y XPP?IK]4@yD mZF[e  (<In brief: Information in this row relates to the residuals, i.e. discrepancies (errors) between the predictions from your fitted model and the observed data. More: For least squares regression, SST=SSR + SSE SST - total sum of squares SSR - regression sum of squares SSE - regression sum of squares (or sum of squares of error). The Residuals row of the ANOVA table deals with the quantities derived from SSE.<(2 (o r~~  <4z XPP?9"]4@4z ̱boN)[<  (<In brief: Information in this row relates to the actual observations. The model does not matter (see More for exceptions). More: For least squares regression, SST=SSR + SSE SST - total sum of squares SSR - regression sum of squares SSE - regression sum of squares (or sum of squares of error). The Total row of the ANOVA table deals with the quantities related to SST. They are generally not affected by the model except by the fact whether the model has a constant - then accounting is done slightly differently (see df commments).<(2 %{(in~~  <z XPP?Z]4@z hPFP3  <In brief: Coefficient Estimates Table provides you with the coefficient estimates and supporting information about the quality of these estimates.<2 T ~~  <z XPP?@']4@z i@D=(  C8<DIn brief: Coefficients estimates of your model terms. More: 1. These are high precision numbers (while the ones in the model equation are not). 2. (Sagata Regression Pro). Note that if you have categorical factors, then "indicator" factors might be introduced thus making this table taller than the Term Significance Table. 3. Coefficient estimates follow normal distribution under idealistic assumptions. Beware: Few decimal digits are displayed for the better look of the output. To retrieve more decimal digits, you should format these cells to display more decimal digits.<82 6(<5Coha~~  <`{ XPP?0)]4@`{ )ґDHyit  8<In brief: Standard errors are the standard deviations of the corresponding coefficient estimates. More: The reported values are the square roots of the diagonal elements of the covariance matrix: var(coefficient_estimate)=inv(X'X)*s^2, where s is the error estimate described in the Summary Statistics Table and X is the design matrix, i.e. an expanded matrix with columns corresponding to each model terms. Beware: Caution mentioned in the Summary Statistics Table with respect to s (error estimate) should be applied when interpreting the standard errors of coefficients. They are again based on idealistic assumptions about your data.<82 b(h5@bon~~  <{ XPP?%-]4@{ OyrA  8<In brief: t-statistic (also called Student's t-statistic) is a standardization of your coefficient estimate for statistical results. More: In this table's context, t-statistic= [Coefficient Estimate] / [Coefficient Error Estimate] The number of degrees of freedom for this t-statistic is: [#of runs - #of model terms] Beware: This estimate is unlikely to exactly follow the t-distribution since the idealistic assumptions are not likely to hold.<82 &(D?5G oti~~  <(| XPP? (]4@(| UvXL ⵏ;  8<In brief: p-value < threshold (commonly, 0.05 is used for the threshold) indicates the importance of the corresponding coefficient. Be advised to check first that ANOVA indicates usefulness of your regression model. More: p-value for t-statistic is the probability that a t-distributed random variable would equal or exceed in absolute value (i.e. 2-tailed) the absolute value of this t-statistic. In other words, it is the probability for the true value of the coefficient to be 0, but still result in a t-statistic equal to or higher than the one you observed. Beware: 1. Be encouraged to use general knowledge in deciding which terms to keep in the model. 2. See general Sagata Help on "multiplicity" effect and why ANOVA is helpful.<82 (45<@ost~~  <| XPP?U +Z]4@|T StG]bf  8<In brief: Lower and Upper 95% are the end points of an interval that contains the true coefficient with 95% chance. This interval is called a 95% Confidence Interval. Rule of thumb: if the interval contains a 0, then the coefficient is not important. More: Confidence Intervals have advantage over p-values because: 1. They imply p-values. If a 95% Confidence Interval contains a 0, it implies that p-value > 0.05. Similarly, if a 95% CI does not contain 0, then p-value < 0.05. 2. They provide info about possible values of the true coefficient. Even if p-value < 0.05, you might decide from Confidence Intervals that still the value of the coefficient is not large enough and declare it unimportant. Beware: 1. 95% is the confidence level for each interval. This confidence level does not apply to all intervals at once, i.e. the statement "all intervals simultaneously contain their respective estimates" does not hold with 95%. This is the "multiplicity effect".<82 (R5oar~~  <| XPP?  +Z]4@|D _@@mB  8<In brief: Lower and Upper 95% are the end points of an interval that contains the true coefficient with 95% chance. This interval is called a 95% Confidence Interval. Rule of thumb: if the interval contains a 0, then the coefficient is not important. More: Confidence Intervals have advantage over p-values because: 1. They imply p-values. If a 95% Confidence Interval contains a 0, it implies that p-value > 0.05. Similarly, if a 95% CI does not contain 0, then p-value < 0.05. 2. They provide info about possible values of the true coefficient. Even if p-value < 0.05, you might decide from Confidence Intervals that still the value of the coefficient is not large enough and declare it unimportant. Beware: 1. 95% is the confidence level for each interval. This confidence level does not apply to all intervals at once, i.e. the statement "all intervals simultaneously contain their respective estimates" does not hold with 95%. This is the "multiplicity effect".<82 (R5ff ~~  <T} XPP? 0']4@T} ;tGNe  8<In brief: VIF (Variance Inflation Factors) show how correlated the model terms are with each other. Rule of thumb: VIF values greater than 10 might alarm you, but the model can still be useful. More: 1. When the constant is in the model, the "traditional" centered VIF are computed. However, when the constant is absent, then uncentered VIF are computed. Be less alarmed by higher than 10 values of uncentered VIF. 2. If the model includes different degrees of the same factor (e.g. x and x^3) or other likely correlated terms, then the VIF factors almost certainly will be much higher than 10, but the model can still be useful. Beware: If the constant is present in the model and is highly correlated with some term, the VIF will not reflect this.<82 ((w5oof~~  <} XPP?26<]4@} vF`JI  <In brief: This table complements the Coefficient Estimates table if your model contains terms with categorical factors by showing contributions of each term.<2 .l ~~  <~ XPP?3;]4@~ ,eL3(¹M  l(<mIn brief: Symbolic names of the terms of your model. More: Terms of the 1st order are represented by the origininal names of the factors as well as automatically assigned "nicknames". For example, if your data had a factor named "Height", X1:Height would include a nickname X1. This nickname would be used to refer to Height in all terms of higher than 1st order.<(2 5(;lic~~  <~ XPP?3C]4@~ VEO}MIB1  8<In brief: Degrees of freedom (df). df of a constant = 0, df of a continuous term = 1 df of a categorical term = depends on this and other model terms. It is sometimes represented by two numbers df1(df2) (see More below) More: df(const)=0 for consistency with traditional ANOVA way of not attributing the constant to the regression model. If you see 2 numbers df1(df2), then df1 is how many degrees of freedom this term contributes in the current model fit and df2 is how many degrees of freedom the model would lose if this term were dropped. If df1=df2, then only one number is shown. Beware: Be careful interpreting the model terms that contain categorical factors. See the Sagata Regression help for more on the specifics of categorical data.<82 (L5Toat~~   <~ XPP?3:]4 @~ eiFFl  (<In brief: SSR_diff - Sum of Squares of Regression Difference. It shows the decrease in SSR of your model if a given term were removed and the reduced model refitted. More: SSR_diff =SSR_full - SSR_reduced, or same, SSR_diff =SSE_reduced - SSE_full<(2 (col~~ ! <H XPP?3 `?-]4!@H =nYAKZS  8<In brief: F-statistic for terms. High value of the F value for a term imply that this term is useful for your model. See also p-value for quantification of what "high" means. More: The formula used is: F= [ SSR_diff/ (df of SSR_diff) ] / [ SSE_full/(df of SSE) ]. See comments in ANOVA table for SSE and its degrees of freedom. Beware: Most statistics (and F-statistic is one of them) are calculated based on idealistic assumptions about your data origins.<82  (M5U@out~~ " < XPP?3 @]4"@T j1@KY'  28<3In brief: p-value < threshold (commonly, 0.05 is used for the threshold) indicates the usefulness of a model term. Be advised to check first that ANOVA indicates usefulness of your regression model. More: p-value for Term Significance is the probability that such high or higher an F value as the one you observed for a given term will be observed for a model that does not include this term. Beware: 1. Be encouraged to use general knowledge in deciding which terms to keep in the model. 2. Interpreting terms with categorical factors is sometimes intricate.<82 (52lm.~~ # <] XPP?AF]4#@]D ڒLdH: kD   < In brief: 3D Plot Engine is used to graphically investigate your fitted model (and your actual system if the model is a good representative). You can: 1. Change the axes for which you want the plot. 2. Change the fixed values of the factors that are not on the axes.<2  o~~ $ <x] XPP?BDx]4$@x] D M[  S<TIn brief: This column contains the names of your factors (or auto-generated names).<2 nSo~~ % <] XPP?B Dx]4%@] qB_u}b  P<QIn brief: Low Values are calculated based on your data (for continuous factors).<2 ]Pod ~~ & <@^ XPP?B@Dx]4&@@^ 4ɱNU(y  Q<RIn brief: High Values are calculated based on your data (for continuous factors).<2 \Qo~~ ' <^ XPP?B Li]4'@^  Ĵ+AŢ۱  [8<\In brief: Use this column to adjust the values of factors that are not on the X or Y axes. More: Experiment with this column. The plot might give you valuable insights into the influence of your factors and their interactions between each other. Beware: Note: the "Fixed" values are still displayed for X-axis, Y-axis factors. They are not used.<82 [(a5[A~~ ( <_ XPP?B N-]4(@_! T^`I *  8<In brief: Click the cells under the "Plot Role" title. Select the role you want for each factor. More: Note that only continuous factors can be placed at the axes. You must make a valid selection for the plot to update, i.e. there should be exactly one "X Axis" and one "Y Axis" with the rest of the factors "Fixed". Beware: The plot will automatically rescale the vertical axis. If you would like to fix the scale, then use Excel features to do so (right mouse click on the vertical axis and choose 1. format axis 2. scale).<82 a(g >5FAchrj ) 0NM@?H`])`"  @""??3` T(` T(` T(` T(` T(@a&3d23 M NM4  3Q:  2.0Q ; Q ; Q3_43_ O   MM<43_ O   MM<43_ O 3f0  MM<43_ O   MM<43_ O *  MM<43_ O +  MM<43_ O   MM<43_ O 3  MM<43_ O f5  MM<4 3_ O   MM<4E4  3Q:  2.4Q ; Q ; Q3_4E4  3Q:  2.9Q ; Q ; Q3_4E4  3Q:  3.3Q ; Q ; Q3_4E4  3Q:  3.8Q ; Q ; Q3_4E4  3Q:  4.2Q ; Q ; Q3_4E4  3Q:  4.7Q ; Q ; Q3_4E4  3Q:  5.1Q ;  Q ; Q3_4E4  3Q:  5.6Q ;  Q ; Q3_4E4  3Q:  6.0Q ;  Q ; Q 3_4E4D $% MP+3O&Q4$% MP+3O&Q4FAWh3OWh3 b+MZ!   43*#M! M  43 #M4%  M3OO&Q  #Bathrooms'4% yIMZ3O8&Q  Price ($)'4%   M3OK&Q  #Bedrooms'43?" :dd444 e????????? ?98?98?98?98?98?98?98?98?98? 98?98@98@98@98@98@98@98@98@98@ 98@VUUUUU@VUUUUU@VUUUUU@VUUUUU@VUUUUU@VUUUUU@VUUUUU@VUUUUU@VUUUUU@ VUUUUU@rq @rq @rq @rq @rq @rq @rq @rq @rq @ rq @88@88@88@88@88@88@88@88@88@ 88@VUUUUU@VUUUUU@VUUUUU@VUUUUU@VUUUUU@VUUUUU@VUUUUU@VUUUUU@VUUUUU@ VUUUUU@88@88@88@88@88@88@88@88@88@ 88@rq@rq@rq@rq@rq@rq@rq@rq@rq@ rq@ @ @ @ @ @ @ @ @ @ @eAhC,͊A7 Ѳ|ApkAkY4ACۯ=xA1%Aڌ@7Oe@ A( :@ A0%f]A AV:BO A>R AF0eZAmbYBA|uA /i1 @ `.@z\V_Au`GM AaTJ A[<AX A. PY A|¢h A^rjA0OA LB8A< wB A+ M7A~':Ap7A_TaA(A(DAGOA=XA ̡狤 AxWqo> AIk|{AMN{A7¿A{CKfAxY4AOK3[AnAS甌VA nAHTQwAJYZACboAƻ_TAB#?z$AwdxzPA+KPp}AxlA7l<A Ձ Aۢ(AXAz#gxAL~)Az;A{WA ?gAýAM`A ȕtAßt AWkA3,-vABGxAP6sEA,Y}ATgHA8A:&̋A jz_AT+!ȼAjf" AwKIAң&A PCA-J=iA/}3NGAuŮ[A0QA FA HAK@ o@ Xmm0+A  ^ A IsA eA 9pzA :@A xFA ي?Ae ~~ * <X XPP?ae<]4*@XT" OtqDDt/Z!X  <In brief: Prediction Engine provides you with an instant prediction from your fitted model. Enter the point where you want to predict and read the results.<2 ~~ + <d XPP?bmK]4+@d" k#M&T  8<In brief: Prediction is the value of your fitted model at the point you specify in the column "Fixed". More: Prediction Engine is a good tool for your system exploration. You might try to start the exploration with the dynamic 3D plot and later validate your conclusions with the Prediction Engine. Beware: Also, look at the Prediction Error to judge the reliability of this prediction.<82 g(m,54d tt~~ , < XPP?cco-]4,@# p΋B)Mƨ  8<In brief: Prediction Error is the standard deviation of the Prediction. More: This error means that if you were to collect new data and refit the model, the prediction estimates would be expected to deviate accordingly to the Prediction Error. It can also be viewed as a long-term error - your averaged system performance would be within the Prediction Error from the Prediction. Beware: If you adopt the recommended settings for your real system, expect higher fluctuations than the Prediction Error in your individual observations.<82 H(N}5 . ~~ - < XPP?dj]4-@$$ ~8JYA  (<In brief: Low and High are calculated based on your data (for continuous factors). More: These values cannot be modified. However, you can still predict outside these ranges.<(2 pT(Zwol~~ . <| XPP?dj]4.@|% xYW@IG9  (<In brief: Low and High are calculated based on your data (for continuous factors). More: These values cannot be modified. However, you can still predict outside these ranges.<(2 mS(Yool~~ / < XPP?d oK]4/@d% ^iDfC+SA  8<In brief: Use the cells in this column to set the factors to the values for which you want to see a prediction. Manually type (for continuous factors) or use droplists (for categorical factors in Sagata Regression Pro). More: You can also predict outside the range of your data points. The warning color will indicate that. Also, pay attention to the increased Prediction Error. 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