ࡱ> DERoot EntryRoot Entry z&@ContentsEmbedding 1 Fz& z&WorkbookF> C !"#$%&'()*+,-./0123456789:;<=>?@ABGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~CompObj fSummaryInformation(DocumentSummaryInformation8XOlePres000[Ole ""X@t飸MKReHeRegress Heade Regre Custo SheetGen UserDGenRegr333333? Regre?Regr333333? Regre? Mod Mode Model Model ModModRegress Regre_3 Regre Sheet UserD RegressRegressionContourPlotOpBodyFatCalculator040Chart Data BodyFatCalculatorBody Fat_3333333?333333???body fat data I!BodyFatCalculatorGenderAgeHeightWeightBody Fat1F1@@Q@]@F2@M@̌[@F2@P@L_@F3@N@]@F3@@P@\@F3@O@Y]@F3@N@a@F3@O@,b@F3@N@33333a@F3@P@ h@F3@O@Yg@F4@@M@fffffX@F4@O@]@F5@P@^@F5@P@33333i@F6@N@fffffV@F6@N@b@F6@O@fffffc@F6@@P@33333e@F7@@P@lg@F8@O@ c@F;@@P@h@F@@M@33333Sc@F@@O@33333d@M3@O@fffffc@M3@@P@33333d@M3@P@33333d@M4@@P@b@M4@P@33333g@M4@@P@g@M4@@P@g@M5@Q@33333b@M5@P@fffff`@M5@P@c@M5@Q@333333f@M5@Q@fffffh@M5@S@33333o@M5@@P@fffffd@M5@P@`c@M5@P@ g@M5@@R@fffffl@M5@P@33333h@M5@P@i@M6@P@fffffb@M6@P@fffffg@M7@P@g@M9@Q@33333h@M;@@Q@yh@M=@P@h@GenderAgeHeightWeightconst K1:Gender X2:Height X3:Weight X1*X2 X2*X312@6@L6@ffffff5@6@L6@L9@33333?@fffff&A@C@33333sD@ffffff,@5@8@C@)@33333=@ A@A@C@L?@ F@B@̌C@.@L2@5@333333/@6@8@8@%@ffffff'@-@333333/@2@3@4@3333334@3333335@fffff9@;@33333>@ffffff-@ffffff=@333336@5@L8@fffff:@RegressionPredictionEngineOpBodyFatCalculatorRUROBody Fat_3333333?333333???body fat data I!BodyFatCalculatorGenderAgeHeightWeightBody Fat1F1@@Q@]@F2@M@̌[@F2@P@L_@F3@N@]@F3@@P@\@F3@O@Y]@F3@N@a@F3@O@,b@F3@N@33333a@F3@P@ h@F3@O@Yg@F4@@M@fffffX@F4@O@]@F5@P@^@F5@P@33333i@F6@N@fffffV@F6@N@b@F6@O@fffffc@F6@@P@33333e@F7@@P@lg@F8@O@ c@F;@@P@h@F@@M@33333Sc@F@@O@33333d@M3@O@fffffc@M3@@P@33333d@M3@P@33333d@M4@@P@b@M4@P@33333g@M4@@P@g@M4@@P@g@M5@Q@33333b@M5@P@fffff`@M5@P@c@M5@Q@333333f@M5@Q@fffffh@M5@S@33333o@M5@@P@fffffd@M5@P@`c@M5@P@ g@M5@@R@fffffl@M5@P@33333h@M5@P@i@M6@P@fffffb@M6@P@fffffg@M7@P@g@M9@Q@33333h@M;@@Q@yh@M=@P@h@GenderAgeHeightWeightconst K1:Gender X2:Height X3:Weight X1*X2 X2*X312@6@L6@ffffff5@6@L6@L9@33333?@fffff&A@C@33333sD@ffffff,@5@8@C@)@33333=@ A@A@C@L?@ F@B@̌C@.@L2@5@333333/@6@8@8@%@ffffff'@-@333333/@2@3@4@3333334@3333335@fffff9@;@33333>@ffffff-@ffffff=@333336@5@L8@fffff:@CxlbaseCntrItem ՜.+,0(HP X`hp x  BodyFatCalculatorChart Data BodyFatCalculatorbody fat data Idata description commentsacknowledgements  WorksheetsOh+'0@V6[ -B   A''  ' A' A' A-  -;@- !;-<@- !<-=@- !=->@- !>-?@- !?---#;#@- !#;-$<$@- !$<-%=%@- !%=-&>&@- !&>-'?'@- !'?---4;4@- !4;-5<5@- !5<-6=6@- !6=-7>7@- !7>-8?8@- !8?---E{E- !E{-F|F- !F|-G}G- !G}-H~H- !H~-II- !I---EE- !E-FF- !F-GG- !G-HH- !H-II- !I---EE- !E-FF- !F-GG- !G-HH- !H-II- !I--  !EAU Arialw@ QwZw0- 72  Prediction Engine (for Body Fat)  Arialw@ QwZw0-2 # Prediction 2 #I24.000982 4Error 2 4I0.782497 Arialw@ QwZw0-2 EVariable  2 ECLow 2 EHigh 2 EFixed-2 VGender  2 VF 2 gAgee  2 gp17 2 g32 2 g252 xHeight  2 xe58.5 2 x76 2 x602 Weight  2 e90.62 252.6 2 120.-"System 0-'-- A-   -"- !"-@@- !@- -""- !"-  -- !-- !-33- !3-#D- !!#-#@D@- !!#@- -#E- !"#-  -#D- !!#- -DD- !D-  -D- !D-EU- !E-E@U@- !E@-EU- !E- -UU- !U-  -EU- !E-B( D"D"-  !@U-  -EU- !E-ff- !f-B( D"D"-  !@f-  -ww- !w-B( D"D"-  !@w-  -- !-B( D"D"-  !@-  -V- !CV-V@@- !CV@-V- !CV-B( D"D"-  !CV- -- !-B( D"D"- !CV-  -- !w-@@- !w@-- !w-- !w-- !w-@@- !@-- !-- !-- !-@@- !@-- !-- !-- !-@@- !@-B- !B-B- !B-""B- !"-33B- !3-DDB- !AD-UUB- !AU-ffB- !Af-wwB- !Aw-B- !A-B- !A-B- !B-B- !B-B- !B-B- !B-B- !B-B- !B-B- !B-!!B- !B!-22B- !B2-CCB- !BC-TTB- !BT-eeB- !Be-vvB- !Bv-B- !B-B- !B-B- !B-B- !B-B- !B-B- !B-B- !B-B- !B-B- !B--'- AA -4 Arialw@  QwZw0-  Arialw@ QwZw0-  Arialw@n IQwZw0- - - - - - - - - - -----' -- --' E-- --'-- UA-Arialw@W 2QwZw0---Arialw@C QwZw0--------'--- UA--  Q<---'--- UA--  $0D)D)#0#0DD0D)#)#0D0-D#-##  qqZZDD0)00))---'--- P<---'--- )0A----'--- &-A--<--  $< ?<9< ---'--- &-A-> $>A>;>---'--- &-A-N $NQNKN---'--- &-A-W $WZWTW---'--- &-A-Z $Z]ZWZ---'--- &-A-b $beb_b---'--- &-A-c $cfc`c---'--- &-A-e $ehebe---'--- &-A-i $ilifi---'--- &-A-i $ilifi---'--- &-A-k $knkhk---'--- &-A-p $pspmp---'--- &-A-q $qtqnq---'--- &-A-t $twtqt---'--- &-A-t $twtqt---'--- &-A-t $twtqt---'--- &-A-t $twtqt---'--- &-A-u $uxuru---'--- &-A-w $wzwtw---'--- &-A-w $wzwtw---'--- &-A-y $y|yvy---'--- &-A-z $z}zwz---'--- &-A-{ ${~{x{---'--- &-A-{ ${~{x{---'--- &-A-} $}}z}---'--- &-A- $~---'--- &-A- $~---'--- &-A- $~---'--- &-A- $---'--- &-A- $---'--- &-A- $---'--- &-A- $---'--- &-A- $---'--- &-A- $---'--- &-A- $---'--- &-A- $---'--- &-A- $---'--- &-A- $---'--- &-A- $---'--- &-A- $---'--- &-A- $---'--- &-A- $---'--- &-A- $---'--- &-A- $||---'--- &-A-z $wz}zw---'--- &-A-u $ruxur---'--- &-A-n $knqnk---'--- &-A-e $beheb---'--- &-A-X $UX[XU---'--- &-A----'--- )0A----'--- UA------'--- ) 0  02 3Normal Scores vs. Residuals        ----'--- UA---'--- UA----'--- UA  2 c-2.5 2 n-2 2 c-1.5 2 n-1 2 c-0.5 2 r01 2 g0.55 2 r11 2 ig1.55 2 Rr21 2 <g2.55---'--- UA---'--- UA  2 +-5 2 05 2 55 2 "10---'--- UA------'--- E. 2 1 Residualsn ----'--- UA-----'--- ' Arialw@ QwZw0-2  Normal Scores-----'--- UA---'--- UA--  Q<--' UA' A '  '--- - ----  -ff- !f-Wf- !W- -WW- !W-Xf- !X- -XX- ! X-Ye- ! Y- -ee- !e-Xe- ! X-  ! Y- -^^ - !^-__ - !_-`` - !`-aa - !a-'--&Sh- - $_\"\"_ $%V^%e--&-- Z:|--- - - -X;- - - - - -   2 =1. - 2 = .- B2 >'Enter your data in the yellowish areas.1            --'-- A--&!6- - $-**- $$,3--&-- &--- - - -$- - - - - -   2 2. - 2  .- 32 Read the body fat prediction.        --'-- A-- ---'NANIHX p | MikefMicrosoft Excel@>"@9v@z& FMicrosoft Excel WorksheetBiff8Excel.Sheet.89q      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcde @\pMike Ba=   ILj =L,p8X@"1Arial1Arial1Arial1Arial1Arial10Arial Unicode MS1Arial10Arial Unicode MS1QTahoma1QTahoma1Arial10Arial Unicode MS1Arial1@Arial1@Arial1QArial1QArial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Tahoma1@Arial1Arial1Arial"$"#,##0_);\("$"#,##0\)!"$"#,##0_);[Red]\("$"#,##0\)""$"#,##0.00_);\("$"#,##0.00\)'""$"#,##0.00_);[Red]\("$"#,##0.00\)7*2_("$"* #,##0_);_("$"* \(#,##0\);_("$"* "-"_);_(@_).))_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)?,:_("$"* #,##0.00_);_("$"* \(#,##0.00\);_("$"* "-"??_);_(@_)6+1_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_)"Yes";"Yes";"No""True";"True";"False""On";"On";"Off" 0.000 0.00000.0                + ) , *  )x +x      h  )8  +8  +<  )x  +x   (  H  @  H  @  H  H  `   H   H        (@             @   @     @@  @  @  (@  `33@ @ +    (  `3@ @+ `BodyFatCalculator$Chart Data BodyFatCalculator5body fat data Idata description%comments3acknowledgements`iz@H5568E3  @@  bGenderAgeHeightWeightBody FatFMGender2=The data might not be representative of any other population.Acknowledgements7Mr. Dana Lee Ling can be reached at dleeling@comfsm.fm:of someone who is not represented well by this population.Comments:Sagata Ltd is thankful for the permission to use the data <to Mr. Dana Lee Ling who is a college teacher in Micronesia. Input factorsLThe data are mostly based on Micronesian students (a Pacific island group). DTanita scale was used to produce the original body fat measurements.4Professional (use Gender2 with the Standard version)Data description&Standard software version can be used.IHowever, the model based on the data may be able to predict the body fat Response(s)<Height (inches). Multiply by 2.54 to convert to centimeters. Age (years).PGender ("M" or "F"). Categorical (text) values are allowed in Sagata Regression 8Weight (lbs). Multiply by 0.454 to convert to kilograms.LGender2 (0 or 1). "0" corresponds to "F" and "1" corresponds to "M" so that @Body fat (%). Body fat measurements produced by a Tanita scale. Output for Body FatRegression EquationlBody Fat = - 97.54 - 13.82*Gender_M + 1.32*Height + 1.11*Weight + 0.00323*Age*Height - 0.0133*Height*Weight 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.ANOVAdfSSMSp-value Regression ResidualsTotalCoefficient Estimates CoefficientsStandard Errort Stat Lower 95% Upper 95%VIFconstGender_M Age*Height Height*WeightTerm SignificancetermSSR_diff013D Plot Engine (for Body Fat)VariableLowHighFixed Plot RoleX AxisY Axis Prediction Engine (for Body Fat) PredictionError Normal ScoresLevels Predictionsk1:Fk1:MAge:17 Age:24.5Age:32 Height:58.5 Height:67.2 Height:76 Weight:90.6 Weight:171.6 Weight:252.6Responsej JKS;,S5RP& @  dMbP?_*+%"??UV      ( )   )! +" +# $,U>t@-򌊶1@-Arҽb@.k$:  6~ E@-;@:*g@-xx=@ 7~ H@-@4ևư@ )8 + +9 +: +; +4 +< += +> -?- 􅻜bX-e6@-Nc*,vkP?-N a-J*I - -@-7[ˤ+-t?M?-p"{1,P_ ;-$|5.-9bt(-sN k? --FTp ?-р?-r @,2Tl%C?-8h'?-x1DB@-8{2U0@ --d}?-;r[?-':ì"@,s:$=-D`>&brRB&p #$%&'()*-./012 -B -*52 - fq]? -@R|֎ ,<^L.> -"2 gO -}kƃ -H݌4תp@ #)C# $+D $+1 $+E $+ $+4 $ %/? %0F %- %- %,- % &/ &0G&,/omS@&-b\s@&,{픲 ; & '/ '0G',DV>M@'-ӭb+@',Fol%C? ' (/ (0G(,Nw@(-֨U@(,f<$= ( )/A )0G),Pf}ss1@)-2@),y7٩? ) */B *0G*,Sۇkm@*-}bMK@*,BL.> * -)H- .+I .+J .+K .8L .8M . /5 /11 /9 /9L / 06031@3@@98@ 09L 1613@M@3S@9P@ 19N 272*@*@9@ 29O"&VVbbbbb&VH88MNOPQRSTU M;PM* NQN2|@8@ ORO47 ? P+I P+J P+K P8L Q" Q Q9 R"R1@@@99@ S"S@M@S@9N@ T"T@@<^@U1111 8****AD(  x  6i XPP? i i]4@i   Ji;ނb a8<bIn brief: Regression Equation shows your fitted model for visual inspection. More: (Sagata Regression Pro). The model might contain extra "indicator" variables that were automatically introduced to treat categorical factors. Beware: Avoid reading the coefficients off of this equation. Refer to the Coefficient Estimates table for more precise values.<82 JM(S56a xx  6,j XPP? iZ]4@,j4  Ƹ{Ftm(X #<$In brief: Summary Statistics table.<2 y#a xx  6j XPP? ix]4@j  !ӶCL8X \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\vxx  6j XPP? i]4@jd  eehA轊dX 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 (Lr@xx  6Xk XPP? ii]4@Xk  'P PJcɘX (<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 (zrxx  6k XPP?  i`]4@k  uUKGCSNX (<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 ( xx  6 l XPP?  ip]4@ l, 㦒WHIcX (<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 &(tlxx  6l XPP?  i@]4@l $;@D#89X 8<In brief: s (estimated error) is an empirical estimate of the repeatability errors in your observations at any point. More: s=sqrt(MSE)=sqrt( SSE/dfE ), where dfE is error degrees of freedom (see comments for ANOVA table or accompanying Help). Under the standard idealistic assumptions, this estimate is an unbiased estimate of the standard deviation of the errors. Beware: Most statistics (and s-estimate is one of them) are calculated based on idealistic assumptions about your data origins. For example, if the regression model is not the same as the true model of your system, then the missed/misrepresented terms will be added to the error estimate.<82 v(|o5wUl xx   6l XPP?  i K]4 @l\ ~) @- X =(<>In brief: The ratio SSE(LSE)/SSE(LAD) can be used as an indicator of outliers. Its values are between 0 ("bad") and 1 ("good"). The values below 0.7 might indicate the presence of influential outliers. More: The ratio of the sum of squared errors (SSE) of the model derived from LSE fitting to the SSE of the model derived from LAD fitting will be close to 1 when both metrics result in similar models. However, if there are influential outliers in the data, then LSE-based model will respond to them more drastically and the SSE(LSE)/SSE(LAD) ratio is likely to decrease.<(2 (=d(xx   6Lm XPP?  i]4 @Lm  ҰvAL"0X t(<uIn brief: The R^1 for LAD metric is analogous to the regular R^2, but in the context of the LAD metric. Its values are also between 0 (bad fit) and 1 (best fit). More: LAD: R^1 has a potential benefit of being more interpretable since it's in the same scale as the response. LAD:R^1 might be compared with R^1 (for LSE) value. See Sagata Help for formulas and references.<(2 (teoxx   6m XPP? i]4 @m }$SOo X 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 (zefxx   6n XPP? i<]4 @n$ ǤaHJWpQX <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  xx   6xn XPP? iK]4 @xn `NmxB(rAm;X (<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( xx  6n XPP? i $<]4@nT  湯DiZo%X 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 ((. a onxx  6@o XPP? i i]4@@o >wmHG- ~X  (< 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 <(  orxx  6o XPP? i ]4@o ("]KRZb) 2X (<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}@ ooxx  6p XPP? i ]4@p {\EObkX _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+_=sexx  6lp XPP? iK]4@lp ҤF:/INl<X @(<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@Sdnxx  6p XPP? i-]4@pL OD(8X (<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 (ldnxx  64q XPP? i!]4@4q ?}A&X (<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 %{( inxx  6q XPP? i<]4@q| -| *L8! X <In brief: Coefficient Estimates Table provides you with the coefficient estimates and supporting information about the quality of these estimates.<2 tsexx  6q XPP? i']4@q L{AQg9X 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(<5C msxx  6`r XPP? i)x]4@`r hj})@ X 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@eonxx  6r XPP? i %]4@rD } 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 (R5lxx  6s XPP? i +<]4@s  CM82vYlX 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 (R5f xx  6Tt XPP? i0']4@Tt a ԣdI.X 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 ((w5e txx  6t XPP? "i&]4@t< b׿1DϥξX <In brief: This table complements the Coefficient Estimates table if your model contains terms with categorical factors by showing contributions of each term.<2 ttxx  6u XPP? #i +]4@u tCVIyf?X 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(;lcouxx  6u XPP? #i3x]4@ul  UM|YeX 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 (L5T t xx   6u XPP? #i *]4 @u |5Ftlxp ) 6NM@?3J])`\"  @MSend with j2 MessengermE,,Letter (8 1/2 x 11 in)"d,,??3` b` b` b` bT` UP%3dJ_23 M NM4  3Q:  90.6Q ; Q ; Q3_43_ O 2  MM<43_ O 3  MM<43_ O 3f0  MM<43_ O   MM<4E4  3Q: 108.6Q ; Q ; Q3_4E4  3Q: 126.6Q ; Q ; Q3_4E4  3Q: 144.6Q ; Q ; Q3_4E4  3Q: 162.6Q ; Q ; Q3_4E4  3Q: 180.6Q ; Q ; Q3_4E4  3Q: 198.6Q ; Q ; Q3_4E4  3Q: 216.6Q ;  Q ; Q3_4E4  3Q: 234.6Q ;  Q ; Q3_4E4  3Q: 252.6Q ;  Q ; Q 3_4E4D$% MP+3O&Q4$% MP+3O&Q4FAOf3OMf3 b+MZ!   43*#M! M  43 #M4% Q 0M3O8&TQ Height'4% ~ 0M3O;&UQ Weight'43?" :dd J'3O K% Mp73OQ4444% 0M3OK&Q Body Fat'44 e@M@@M@@M@@M@@M@@M@@M@@M@@M@ @M@88N@88N@88N@88N@88N@88N@88N@88N@88N@ 88N@q1O@q1O@q1O@q1O@q1O@q1O@q1O@q1O@q1O@ q1O@UUUUUP@UUUUUP@UUUUUP@UUUUUP@UUUUUP@UUUUUP@UUUUUP@UUUUUP@UUUUUP@ UUUUUP@qǑP@qǑP@qǑP@qǑP@qǑP@qǑP@qǑP@qǑP@qǑP@ qǑP@88Q@88Q@88Q@88Q@88Q@88Q@88Q@88Q@88Q@ 88Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@ Q@rqR@rqR@rqR@rqR@rqR@rqR@rqR@rqR@rqR@ rqR@98R@98R@98R@98R@98R@98R@98R@98R@98R@ 98R@ S@ S@ S@ S@ S@ S@ S@ S@ S@ S@eji?qC@ 53X-)@, Z2@̉X 8@hA>@vVB@TXFYE@(a\H@ g8_K@LzV?͈@(a$(@>Ö1@VMt%7@[%<@] 5k!A@n5@ a<1B8@ `rǽ-@ a/@@ ~ M@ f"@ n*&@ `X'/*@ ݆-@ 0@ _q2@ *r4@e xx * 6} XPP? Li0P]4*@}" \ D{:B+pX <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 xx + 6(~ XPP? MiX-]4+@(~# oZE3킮jX 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@ xx , 6x~ XPP? NiZ]4,@x~$$ ]\ %KʟϕX 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}5orxx - 6~ XPP? OiT]4-@~$ X%nIx}^ X (<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(Zcolxx . 6@ XPP? OiT]4.@@T% 8'PLE X (<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(Yrolxx / 6 XPP? Oi `Z-]4/@% bNBoX 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. Beware: No warnings.<82 (|5Iel xp 0 6NM@?Wk]0`&  @"&??3` 9e` 9e` 9e` 9e` 9e3d23 M NM4 113QQ ;1 Q ;1 Q3_4E4D $% MP+3O&Q4$% MP+3O&Q4FA) 3Otj 3*#M43*#M4% DM3OA&Q  Residuals'4% (MZ3Oa&Q  Normal Scores'4523 M  43d" 3_ M NM  MM<444% )UN ^M3O&Q :Normal Scores vs. Residuals'441e+0:LāK{ hd0w$NM0J, 0Wc "F" {!&  P/2F hC `lff`lffb9G%3z`R,c@}`3 <3؇g߿X<ݿֿrZ=[5`#%,ptI?``P??lM? 栅i?! gyFZr?"@9 ?#?$4[a?%@1?&Xg?'%??(mM?)WK?*@7d(@+Ry@,u)TA@->͊.Z@.H\ @/LywY|@0PSx@e\Cm!u9#J{hoHmDJ  c ?ܵ F%u  J{/L@tݿffffffڿlֿZd;OӿK46пɿSÿݵ|гݵ|гݵ|г?ݵ|г?S??K46?Zd;O?l? ffffff?!t?"@?#J{/L?$?% F%u?&?ܵ?' c?(DJ?)m?*H?+?,ho?-9#J{?.!u?/?0\Cm@e xp 1 6NM@?l ]1`'  @"'??3` (e` (e` (e` (e` (e3d23 M NM4 3QQ ;4AQ ;4AQ3_  NM  d43_ M NM  d43_ M NM  d4E4D $% MP+3O&Q4$% MP+3O&Q4FAY 3Ot 3 b MZ43*#M4%  M3O2&Q Factors'4% ?N#MZ3O&Q (Predicted Response'4523 M  43" 3_ M NM  MM<444% U^M3OZ&Q \,Pseudo Main Effects Plot - Model Predictions'44ek1:Fk1:M Age:17 Age:24.5Age:32   Height:58.5 Height:67.2 Height:76  ! Weight:90.6 ! Weight:171.6! Weight:252.6edJw@@؀癈3@@09@N:@hdr<@Yj GA@N:@ c3@  UlC"@ N:@ |yb@F@e xp 2 6NM@?]2`'  @"'??3` 9e ` 9e!` 9e"` 9e#` 9e$3d23 M NM4 113QQ ;4dQ ;4dQ3_4E4D $% MP+3O& Q4$% MP+3O&!Q4FA 3Otj 3*#M43*#M4%  wM3OE&$Q  Prediction'4% (MZ3OA&#Q  Residuals'4523 M  43d" 3_ M NM  MM<444% U ^M3O&"Q 4Residuals vs. Prediction'441e)}3@y3@`/7@@֙K5@LU4@9y5@ԭXz=@|+=@x7n=@ JNiXC@ h*A D@ t(10@ 璘5@ $r87@%~J E@Df,@e#/@@rZT$@@`'9A@rϩC@Dt^@@`]@E@,}pB@b因C@+s71@j^53@h[Bo2@R3,@ş 6@049@049@>b߲)@ `@eaL)&@!(ъr0@" 3@#`bU5@$a3@%PS3@&9(b/@'@(VW6@(Nzv6@)8s:@*1ı=@+0jg'o.@, :@-H6mm7@.`#%5@/7@0WZ;@ehC@7d(@`R,cr@1? gyFZr?+0u)TA@PSx@ 3؇g߿ @} $NM ֿ %??0w0WchdWK?4[a?Z=[5{!& mM?%3z@9 ?J, `3Ry@Xg?栅i?`lff`lff0 ``P?!"F"":Lā#K{ $ %lM?&LywY|@'P/2F(H\ @),ptI?*?+<,>͊.Z@-b9G.`#%/?0X<ݿe xp 3 6NM@? ]3`L(  @"L(??3` 9e%` 9e&` 9e'` 9e(` 9e)3d23 M NM4 3QQ ;55Q ;44Q3_ M NM  d4E4 3QQ ;66Q ;44Q3_ M NM  d4E4 3QQ ;77Q ;44Q3_ M NM  d4E4 3QQ ;88Q ;44Q3_ M NM  d4E4 3QQ ;99Q ;44Q3_ M NM  d4E4 3QQ ;::Q ;44Q3_ M NM  d4E4 3QQ ;;;Q ;44Q3_ M NM  d4E4 3QQ ;<<Q ;44Q3_ M NM  d4E4 3QQ ;==Q ;44Q3_ M NM  d4E4 3QQ ;>>Q ;44Q 3_ M NM  d4E4 3QQ ;??Q ;44Q 3_ M NM  d4E4 3QQ ;@@Q ;44Q 3_ M NM  d4E4 3QQ ;AAQ ;44Q 3_ M NM  d4E4 3QQ ;BBQ ;44Q 3_ M NM  d4E4 3QQ ;CCQ ;44Q3_ M NM  d4E4 3QQ ;DDQ ;44Q3_ M NM  d4E4 3QQ ;EEQ ;44Q3_ M NM  d4E4 3QQ ;FFQ ;44Q3_ M NM  d4E4 3QQ ;GGQ ;44Q3_ M NM  d4E4 3QQ ;HHQ ;44Q3_ M NM  d4E4 3QQ ;IIQ ;44Q3_ M NM  d4E4 3QQ ;JJQ ;44Q3_ M NM  d4E4 3QQ ;KKQ ;44Q3_ M NM  d4E4 3QQ ;LLQ ;44Q3_ M NM  d4E4 3QQ ;MMQ ;44Q3_ M NM  d4E4D $% MP+3O&%Q4$% MP+3O&&Q4FAB 3Otj 3 b#M43*#M4% M3O3&)Q Gender'4% (MZ3OA&(Q  Residuals'4523 M  43" 3_ M NM  MM<444% Uq^M3O&'Q ,Residuals vs. Gender'44e F F F F F F F F F F F F F F F F F F F F F F F F F M M M M M M M M M  M  M  M  M  M M M M M M M M M M M MehC@7d(@`R,cr@1? gyFZr?+0u)TA@PSx@ 3؇g߿ @} $NM ֿ %??0w0WchdWK?4[a?Z=[5{!& mM?%3z@9 ?J, `3Ry@Xg?栅i?`lff`lff0``P? "F" :Lā K{   lM?LywY|@P/2FH\ @,ptI??<>͊.Z@b9G`#%?X<ݿe xp 4 6NM@?]4`(  @"(??3` 9e*` 9e+` 9e,` 9e-` 9e.3d23 M NM4 113QQ ;4d Q ;4d Q3_4E4D $% MP+3O&*Q4$% MP+3O&+Q4FA 3Otj 3*#M43*#M4%  uM3O&.Q  Age'4% (MZ3OA&-Q  Residuals'4523 M  43d" 3_ M NM  MM<444% 8U"^M3O&,Q &Residuals vs. Age'441e1@2@2@3@3@3@3@3@3@ 3@ 3@ 4@ 4@ 5@5@6@6@6@6@7@8@;@@@@@3@3@3@4@4@4@4@5@ 5@!5@"5@#5@$5@%5@&5@'5@(5@)5@*5@+6@,6@-7@.9@/;@0=@ehC@7d(@`R,cr@1? gyFZr?+0u)TA@PSx@ 3؇g߿ @} $NM ֿ %??0w0WchdWK?4[a?Z=[5{!& mM?%3z@9 ?J, `3Ry@Xg?栅i?`lff`lff0 ``P?!"F"":Lā#K{ $ %lM?&LywY|@'P/2F(H\ @),ptI?*?+<,>͊.Z@-b9G.`#%/?0X<ݿe xp 5 6NM@? ]5`|)  @"|)??3` 9e/` 9e0` 9e1` 9e2` 9e33d23 M NM4 113QQ ;gQ ;gQ3_4E4D $% MP+3O&/Q4$% MP+3O&0Q4FA 3Otj 3*#M43*#M4% CM3O-&3Q Height'4% (MZ3OA&2Q  Residuals'4523 M  43d" 3_ M NM  MM<444% U$^M3O&1Q ,Residuals vs. Height'441e@Q@M@P@N@@P@O@N@O@N@ P@ O@ @M@ O@ P@P@N@N@O@@P@@P@O@@P@M@O@O@@P@P@@P@P@@P@@P@Q@ P@!P@"Q@#Q@$S@%@P@&P@'P@(@R@)P@*P@+P@,P@-P@.Q@/@Q@0P@ehC@7d(@`R,cr@1? gyFZr?+0u)TA@PSx@ 3؇g߿ @} $NM ֿ %??0w0WchdWK?4[a?Z=[5{!& mM?%3z@9 ?J, `3Ry@Xg?栅i?`lff`lff0 ``P?!"F"":Lā#K{ $ %lM?&LywY|@'P/2F(H\ @),ptI?*?+<,>͊.Z@-b9G.`#%/?0X<ݿe xp 6 6NM@?]6`*  @"*??3` 9e4` 9e5` 9e6` 9e7` 9e83d23 M NM4 113QQ ;gQ ;gQ3_4E4D $% MP+3O&4Q4$% MP+3O&5Q4FA 3Otj 3*#M43*#M4% |vM3O1&8Q Weight'4% (MZ3OA&7Q  Residuals'4523 M  43d" 3_ M NM  MM<444% UJ^M3O&6Q ,Residuals vs. Weight'441e]@̌[@L_@]@\@Y]@a@,b@33333a@ h@ Yg@ fffffX@ ]@ ^@33333i@fffffV@b@fffffc@33333e@lg@ c@h@33333Sc@33333d@fffffc@33333d@33333d@b@33333g@g@g@33333b@ fffff`@!c@"333333f@#fffffh@$33333o@%fffffd@&`c@' g@(fffffl@)33333h@*i@+fffffb@,fffffg@-g@.33333h@/yh@0h@ehC@7d(@`R,cr@1? gyFZr?+0u)TA@PSx@ 3؇g߿ @} $NM ֿ %??0w0WchdWK?4[a?Z=[5{!& mM?%3z@9 ?J, `3Ry@Xg?栅i?`lff`lff0 ``P?!"F"":Lā#K{ $ %lM?&LywY|@'P/2F(H\ @),ptI?*?+<,>͊.Z@-b9G.`#%/?0X<ݿe xp 7 6NM@? ]7`*  @"*??3` 9e9` 9e:` 9e;` 9e<` 9e=3d23 M NM4 113QQ ;gQ ;gQ3_4E4D $% MP+3O&9Q4$% MP+3O&:Q4FA 3Otj 3*#M43*#M4% <DM3OA&=Q Response'4% #(BMZ3OE&<Q  Prediction'4523 M  43d" 3_ M NM  MM<444% U ^M3O&;Q 2Prediction vs. Response'441e2@6@L6@ffffff5@6@L6@L9@33333?@fffff&A@ C@ 33333sD@ ffffff,@ 5@ 8@C@)@33333=@ A@A@C@L?@ F@B@̌C@.@L2@5@333333/@6@8@8@%@ ffffff'@!-@"333333/@#2@$3@%4@&3333334@'3333335@(fffff9@);@*33333>@+ffffff-@,ffffff=@-333336@.5@/L8@0fffff:@e)}3@y3@`/7@@֙K5@LU4@9y5@ԭXz=@|+=@x7n=@ JNiXC@ h*A D@ t(10@ 璘5@ $r87@%~J E@Df,@e#/@@rZT$@@`'9A@rϩC@Dt^@@`]@E@,}pB@b因C@+s71@j^53@h[Bo2@R3,@ş 6@049@049@>b߲)@ `@eaL)&@!(ъr0@" 3@#`bU5@$a3@%PS3@&9(b/@'@(VW6@(Nzv6@)8s:@*1ı=@+0jg'o.@, :@-H6mm7@.`#%5@/7@0WZ;@e xp 8 6NM@?]8`D+  @"D+??3` 9e>` 9e?` 9e@` 9eA` 9eB3d23 M NM4 3QQ ;hh Q ;gg Q3_ M NM  d4E4 3QQ ;ii Q ;gg Q3_ M NM  d4E4 3QQ ;jj Q ;gg Q3_ M NM  d4E4 3QQ ;kk Q ;gg Q3_ M NM  d4E4 3QQ ;ll Q ;gg Q3_ M NM  d4E4 3QQ ;mm Q ;gg Q3_ M NM  d4E4 3QQ ;nn Q ;gg Q3_ M NM  d4E4 3QQ ;oo Q ;gg Q3_ M NM  d4E4 3QQ ;pp Q ;gg Q3_ M NM  d4E4 3QQ ;qq Q ;gg Q 3_ M NM  d4E4 3QQ ;rr Q ;gg Q 3_ M NM  d4E4 3QQ ;ss Q ;gg Q 3_ M NM  d4E4 3QQ ;tt Q ;gg Q 3_ M NM  d4E4 3QQ ;uu Q ;gg Q 3_ M NM  d4E4 3QQ ;vv Q ;gg Q3_ M NM  d4E4 3QQ ;ww Q ;gg Q3_ M NM  d4E4 3QQ ;xx Q ;gg Q3_ M NM  d4E4 3QQ ;yy Q ;gg Q3_ M NM  d4E4 3QQ ;zz Q ;gg Q3_ M NM  d4E4 3QQ ;{{ Q ;gg Q3_ M NM  d4E4 3QQ ;|| Q ;gg Q3_ M NM  d4E4 3QQ ;}} Q ;gg Q3_ M NM  d4E4 3QQ ;~~ Q ;gg Q3_ M NM  d4E4 3QQ ; Q ;gg Q3_ M NM  d4E4 3QQ ; Q ;gg Q3_ M NM  d4E4D $% MP+3O&>Q4$% MP+3O&?Q4FA 3Otj 3 b#M43*#M4% M3O3&BQ Gender'4% S(MZ3O<&AQ Body Fat'4523 M  43" 3_ M NM  MM<444% U^M3O&@Q *Body Fat vs. Gender'44e F F F F F F F F F F F F F F F F F F F F F F F F F M M M M M M M M M  M  M  M  M  M M M M M M M M M M M Me2@6@L6@ffffff5@6@L6@L9@33333?@fffff&A@ C@ 33333sD@ ffffff,@ 5@ 8@C@)@33333=@ A@A@C@L?@ F@B@̌C@.@L2@5@333333/@6@8@8@%@ffffff'@ -@ 333333/@ 2@ 3@ 4@3333334@3333335@fffff9@;@33333>@ffffff-@ffffff=@333336@5@L8@fffff:@e xp 9 6NM@? ]9`+  @"+??3` 9eC` 9eD` 9eE` 9eF` 9eG3d23 M NM4 113QQ ;Q ;Q3_4E4D $% MP+3O&CQ4$% MP+3O&DQ4FA 3Otj 3*#M43*#M4% $uM3O&GQ  Age'4% S(MZ3O<&FQ Body Fat'4523 M  43d" 3_ M NM  MM<444% lU^M3O&EQ $Body Fat vs. Age'441e1@2@2@3@3@3@3@3@3@ 3@ 3@ 4@ 4@ 5@5@6@6@6@6@7@8@;@@@@@3@3@3@4@4@4@4@5@ 5@!5@"5@#5@$5@%5@&5@'5@(5@)5@*5@+6@,6@-7@.9@/;@0=@e2@6@L6@ffffff5@6@L6@L9@33333?@fffff&A@ C@ 33333sD@ ffffff,@ 5@ 8@C@)@33333=@ A@A@C@L?@ F@B@̌C@.@L2@5@333333/@6@8@8@%@ ffffff'@!-@"333333/@#2@$3@%4@&3333334@'3333335@(fffff9@);@*33333>@+ffffff-@,ffffff=@-333336@.5@/L8@0fffff:@e xp : 6NM@?]:`t,  @"t,??3` 9eH` 9eI` 9eJ` 9eK` 9