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{"sheet":"Linear regression","index":2,"n_rows":436,"n_cols":13,"rows_kept":436,"cut":false,"hidden":false,"merged":[[419,1,420,9],[425,1,426,8],[428,1,430,8],[432,1,434,8],[435,1,436,8]]}
[null,"XLSTAT 2024.2.2.1422 - Linear regression - Start time: 08/12/2024 at 20:20:59 / End time: 08/12/2024 at 20:21:01 / Microsoft Excel 16.017830"]
[null,"Y / Dependent variables: Workbook = demo01MultiReg (2).xlsm / Sheet = Data / Range = 'Data'!$D:$D / 237 rows and 1 column"]
[null,"X / Quantitative: Workbook = demo01MultiReg (2).xlsm / Sheet = Data / Range = 'Data'!$B:$C / 237 rows and 2 columns"]
[null,"Confidence interval (%): 95"]
[null,"Tolerance: 0.0001"]
[]
[]
[]
[]
[null,"Summary statistics:"]
[]
[null,"Variable","Observations","Obs. with missing data","Obs. without missing data","Minimum","Maximum","Mean","Std. deviation"]
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[null,"Height",237,0,237,50.5,72,61.364556962025326,3.9454018927428063]
[]
[]
[null,"Correlation matrix:"]
[]
[null,null,"Age","Height","Weight"]
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[null,"Height",0.64885679329870105,1,0.77487610662760165]
[null,"Weight",0.63463642943829845,0.77487610662760165,1]
[]
[]
[null,"Multicolinearity statistics:"]
[]
[null,null,"Age","Height"]
[null,"Tolerance",0.57898486179012676,0.57898486179012676]
[null,"VIF",1.7271608741343654,1.7271608741343654]
[]
[]
[null,"Regression of variable Weight:"]
[]
[null,"Goodness of fit statistics (Weight):"]
[]
[null,"Observations",237]
[null,"Sum of weights",237]
[null,"DF",234]
[null,"R²",0.63045995194361859]
[null,"Adjusted R²",0.6273014899944187]
[null,"MSE",140.85795087044181]
[null,"RMSE",11.868359232448343]
[null,"MAPE",9.0487589882859982]
[null,"DW",2.1774002842852687]
[null,"Cp",3]
[null,"AIC",1175.5980611290122]
[null,"AICC",1175.7010654208577]
[null,"SBC",1186.0022415524177]
[null,"PC",0.3790154339039809]
[null,"Press",33967.233985967105]
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[]
[]
[null,"Analysis of variance (Weight):"]
[]
[null,"Source","DF","Sum of squares","Mean squares","F","Pr > F","p-values signification codes"]
[null,"Model",2,56233.254264249161,28116.62713212458,199.60979808648264,2.6085356790148159E-51,"***"]
[null,"Error",234,32960.760503683385,140.85795087044181,null,null,""]
[null,"Corrected Total",236,89194.014767932546,null,null,null,""]
[null,"Computed against model Y=Mean(Y)"]
[null,"Signification codes: 0 < *** < 0.001 < ** < 0.01 < * < 0.05 < . < 0.1 < ° < 1"]
[]
[]
[null,"Type I Sum of Squares analysis (Weight):"]
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[null,"Source","DF","Sum of squares","Mean squares","F","Pr > F","p-values signification codes"]
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[]
[]
[null,"Type III Sum of Squares analysis (Weight):"]
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[null,"Signification codes: 0 < *** < 0.001 < ** < 0.01 < * < 0.05 < . < 0.1 < ° < 1"]
[]
[]
[null,"Model parameters (Weight):"]
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[null,"Source","Value","Standard error","t","Pr > |t|","Lower bound (95%)","Upper bound (95%)","p-values signification codes"]
[null,"Intercept",-127.81990744476943,12.098996100380022,-10.564505218805277,1.3879489047370702E-21,-151.65678868402279,-103.98302620551607,"***"]
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[null,"Signification codes: 0 < *** < 0.001 < ** < 0.01 < * < 0.05 < . < 0.1 < ° < 1"]
[]
[]
[null,"Equation of the model (Weight):"]
[]
[null,"Weight = -127.819907444769+0.240274914264461*Age+3.09004803935285*Height"]
[]
[]
[null,"Standardized coefficients (Weight):"]
[]
[null,"Source","Value","Standard error","t","Pr > |t|","Lower bound (95%)","Upper bound (95%)","p-values signification codes"]
[null,"Age",0.22773100367505833,5.2226295585174956E-2,4.3604663345049204,1.9455415206870441E-5,0.12483717718718508,0.33062483016293159,"***"]
[null,"Height",0.62711129784830855,5.2226295585174942E-2,12.007577616252025,0,0.52421747136043528,0.73000512433618181,"***"]
[null,"Signification codes: 0 < *** < 0.001 < ** < 0.01 < * < 0.05 < . < 0.1 < ° < 1"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null," "]
[]
[]
[null,"Predictions and residuals (Weight):"]
[]
[null,"Observation","Weight","Weight","Pred(Weight)","Residual","Std. residual","Std. dev. on pred. (Mean)","Lower bound 95% (Mean)","Upper bound 95% (Mean)","Std. dev. on pred. (Observation)","Lower bound 95% (Observation)","Upper bound 95% (Observation)"]
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[null,"Obs8",1,140,125.03597112837936,14.964028871620641,1.260833833771114,2.1364189741196373,120.82689750434722,129.2450447524115,12.059114266952619,101.27766322852752,148.79427902823119]
[null,"Obs9",1,110.5,106.6711437110238,3.8288562889761977,0.32261041429450704,1.6496799179675812,103.42102081147685,109.92126661057075,11.982461963310683,83.063852626407609,130.27843479563998]
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[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null," "]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null," "]
[]
[]
[null,"Test assumptions:"]
[]
[null,"Test on the normality of the residuals (Shapiro-Wilk) (Weight):"]
[]
[null,"W",0.95906510961651337]
[null,"p-value (Two-tailed)",2.7722894087034433E-6,"***"]
[null,"alpha",0.05]
[null,"Signification codes: 0 < \"***\" < 0.001 < \"**\" < 0.01 < \"*\" < 0.05 < \".\" < 0.1 < \" \" < 1"]
[]
[null,"Test interpretation:"]
[null,"H0: The residuals follow a Normal distribution."]
[null,"Ha: The residuals do not follow a Normal distribution."]
[null,"As the computed p-value is lower than the significance level alpha=0.05, one should reject the null hypothesis H0, and accept the alternative hypothesis Ha."]
[]
[]
[]
[null,"Interpretation (Weight):"]
[]
[null,"Given the R2, 63% of the variability of the dependent variable Weight is explained by the 2 explanatory variables."]
[]
[]
[null,"Given the p-value of the F statistic computed in the ANOVA table, and given the significance level of 5%, the information brought by the explanatory variables is significantly better than what a basic mean would bring."]
[]
[]
[]
[null,"Based on the Type III sum of squares, the following variables bring significant information to explain the variability of the dependent variable Weight: Age,Height."]
[]
[]
[null,"Among the explanatory variables, based on the Type III sum of squares, variable Height is the most influential."]

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