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Data SheetScatter Diagrami%Simple Regression
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+C;Tool Life versus Cutting SpeedYTool Life, minutesCutting Speed, ft/minX,Y = mX + b where m = slope and b = interceptb=b= YBar  mXBarAverageXXBarSumYYbar(XXbar)(YYbar))m = Sum((XXBar)(YYBar))/Sum((XXBar)^2)
(XXbar)^2=m=>r = Sum((XXbar)(YYbar))/SQRT(Sum((XXbar)^2)Sum((YYbar)^2))r=
(YYbar)^2r^2=SUMMARY OUTPUTRegression Statistics
Multiple RR SquareAdjusted R SquareStandard ErrorObservationsANOVA
RegressionResidualTotal InterceptdfSSMSFSignificance FCoefficientst StatPvalue Lower 95% Upper 95%Lower 95.0%Upper 95.0%RESIDUAL OUTPUTObservationPredicted Y ResidualsStandard ResidualsPROBABILITY OUTPUT
Percentile0Simple Regression using the Least Squares MethodExcel ANOVA ExplainedtThis sheet is an attempt by William Menzl to understand the calculations and meaning behind the data provided in theoANOVA report generated using the Regression Function in Microsoft Excel. Data and interpretation were obtainedqfrom Juran's Quality Control Handbook, Fourth Edition pages 23.96 through 23.108. The information in the text isNexcellent and this sheet is not meant to replace the explanations of the book.&Most Important Statistics are in bold.BM[W
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MS is the Mean Square (Mean or average of the sum of squares) and is calculated by dividing the Sum of Squares by the degrees of freedom.<xx
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Multiple Coorelation coefficient  Esentially useless<F~~
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Proportion of variation explained by a regression model. Square of sample multiple correlation coefficient (Multiple R above)
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This F(calculated) value is MS Regression divided by MS Residual<QMxx
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Estimate of the variance (s^2) of Y about the regression line.<O~~
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The value below [F(calculated)] can be compared with an F table using the degrees of freedom for Regression and Residual and with a suitable confidence value (0.95). If F(calculated) is greater than F(Table), the conclusion is that the regression is significant and that the prediction (regression) equation is a better predictor of Y than YBar.
This comparrison is already done by the computer and the probability is shown as the Significance F to the right. Read the Significance F note for details on the value shown.<xx
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This is the intercept of the regession line or (b) in Y=mX + b.<Pxx
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This is the slope of the regession line or (m) in Y=mX+b.<J~~
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This is the degrees of freedom. One degree of freedom for every factor in the regression equation and the remainder are residual degrees of freedom. The total degrees of freedom equals n1 (observations  1).< ~~
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This is the probability that the F value calculated to the left is insignificant. Multiply this value by 100 to get the % of insignificance. This value is the probability from the F tables using the F value to the left and the degrees of Freedom for Regression and Residual. Low values are desired (less than 0.05) as this will result in significant regression models.<:'~~
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This value is calculated as Sum((YYbar)^2) and is called the total sum of squares. This calculation of this value is detailed in the Simple Regression tab.<~~
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This is the sum of squares due to regression and is calculated using the slope of the regression line. Calculation is
SS(Reg) = m*Sum((XXbar)*(YYbar))<~~
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The sum of squares residual is calculated by taking the Total Sum of squares (below) and subtracting the Sum of Squares due to regression (above).<~~
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This is the square root of the residual Mean Square (Estimate of the variance of Y about the regression line) and is the standard deviation of Y about the regression line. Units are the same as the units of Y.<(Xxx
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This is the number of data points (n) used in the regression model.<T))~~
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This is often called the standard error of the regression coefficient and is = s/Sqrt(Sum((XXbar)^2)) where s is the Standard Error found above.<~~
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These values are the coefficient divided by the Standard Error are are the calculated t statistic (tcalc). These values can be compared against a ttable using a suitable acceptance criteria. This comparrison has already been completed by the program with the data shown under pvalue.<0~~
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This p valus is the probability that the variable is insignificant. Multiply the value by 100 for percent of insignificance. The desired values (alpha value) will be low, generally less than 0.05 or 5%. Values greater than the alpha value indicate that the varible does not effect the outcome and you should consider taking the variable out of the regresssion equation. Note: pvalue reported is 1 (pvalue) that is shown in most ttables.< WILLIAM M MENZLaWILLIAM M MENZLaWILLIAM M MENZLaWILLIAM M MENZLa
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CreditsData SheetSimple RegressionANOVAScatter DiagramWorksheetsCharts
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