Model-Building.pptx

CHAPTER 17Model Buildingto accompanyIntroduction to Business Statisticsfourth edition,by Ronald M.WeiersPresentation by Priscilla Chaffe-Stengel Donald N.Stengel 2002 The Wadsworth GroupChapter 17-Learning ObjectivesBuild polynomial regression models to describe curvilinear relationshipsApply qualitative variables representing two or three categories.Use logarithmic transforms in constructing exponential and multiplicative models.Identify and compensate for multicollinearityApply stepwise regressionSelect the most suitable among competing models 2002 The Wadsworth GroupPolynomial Models with One Quantitative Predictor VariableSimple linear regression equation:Equation for second-order polynomial model:Equation for third-order polynomial model:Equation for general polynomial model:2002 The Wadsworth GroupPolynomial Models with Two Quantitative Predictor VariablesFirst-order model with no interaction:First-order model with interaction:Second-order model with no interaction:Second-order model with interaction:2002 The Wadsworth GroupModels with Qualitative VariablesEquation for a model with a categorical independent variable with two possible states:where state 1 is shown x=1where state 2 is shown x=0Equation for a model with a categorical independent variable with three possible states:where state 1 is shown x1=1,x2=0where state 2 is shown x1=0,x2=1Where state 3 is shown x1=0,x2=0 2002 The Wadsworth GroupModels with Data TransformationsExponential Model:General equation for an exponential model:Corresponding linear regression equation for an exponential model:Multiplicative Model:General equation for a multiplicative model:Corresponding linear regression equation for a multiplicative model:2002 The Wadsworth GroupExample,Problem 17.8International Data Corporation has reported the following costs per gigabyte of hard drive storage space for years 1995 through 2000.Using x=1 through 6 to represent years 1995 through 2000,fit a second-order polynomial model to the data and estimate the cost per gigabyte for the year 2008.The regression equation will have the form:Yearx=Yry=Cost19951$261.8419962137.941997369.681998429.301999513.09200066.46 2002 The Wadsworth GroupExample,Problem 17.8,cont.Microsoft Excel Output 2002 The Wadsworth GroupSUMMARY OUTPUTRegression StatisticsMultiple R0.99655892R Square0.99312968Adj R Square0.98854948Standard Error 10.5650522Observations 6Example,Problem 17.8,cont.Microsoft Excel Output The regression equation is:2002 The Wadsworth GroupCoefficientsStandardErrort StatP-valueIntercept387.99318.899339920.5294470.0002527x-147.6567512.3644646-11.942030.0012629x214.18839291.729112558.20559240.0037879Example,Problem 17.8,cont.To estimate the cost per gigabyte for the year 2008,evaluate when x=14.So the cost per gigabyte in 2008 is estimated to be$1101.99.Does this make sense?Of course not.Explanation:Although the polynomial equation provides a good fit for the data during the period 1995-2000,this form is not appropriate to extrapolate the data out to 2008.2002 The Wadsworth GroupExample,Problem 17.32An exponential model will probably be more appropriate to the data used in Problem 17.8.2002 The Wadsworth GroupyLog yx$261.842.4180361137.942.13969269.681.843108329.301.466868413.091.1169456.460.8102336Example,Problem 17.32,cont.Microsoft Excel Output 2002 The Wadsworth GroupSUMMARY OUTPUTRegression StatisticsMultiple R0.998899423R Square0.997800057Adj R Square0.997250071Standard Error 0.03222401Observations 6Example,Problem 17.32,cont.Microsoft Excel Output The regression equation is:2002 The Wadsworth GroupCoefficientsStandardErrort StatP-valueIntercept 2.7808299850.0299989292.697678.12E-08x-0.328100280.00770301-42.59381.82E-06Example,Problem 17.32,cont.For x=14,Based on the exponential model,the cost per gigabyte in 2008 will be$0.0154,or just under 2 cents.2002 The Wadsworth GroupExample,Problem 17.27An efficiency expert has studied 12 employees who perform similar assembly tasks,recording productivity(units per hour),number of years of experience,and which one of three popular assembly methods the individual has chosen to use in performing the task.Given the data,shown on the next slide,determine the linear regression equation for estimating productivity based on the other variables.For any qualitative variables that are used,be sure to specify the coding strategy each will employ.2002 The Wadsworth GroupExample,Problem 17.27,cont.2002 The Wadsworth GroupWorkerProd.Yrs.ExpMethodWorkerProd.Yrs.ExpMethod175 7A79712B28810C88510C391 4B910212C493 5B109313A59511C1111212B677 3A128614AExample,Problem 17.27,cont.The equation for a model with one quantitative variable and a categorical independent variable with three possible states is:where x1 represents the years of experiencewhere state 1 is shown x2=1 if method A is used,0 if otherwisewhere state 2 is shown x3=1 if method B is used,0 if otherwisewhere state 3 is shown x2=0 and x3=0 if method C is used.2002 The Wadsworth GroupExample,Problem 17.27,cont.So the data to be analyzed are:2002 The Wadsworth GroupWorkeryx1x2x3175 7102881000391 401493 5015951100677 310Example,Problem 17.27,cont.2002 The Wadsworth GroupWorkeryx1x2x37 9712018 8510009102120010 93131011112120112 861410Example,Problem 17.27,cont.Microsoft Excel Output 2002 The Wadsworth GroupSUMMARY OUTPUTRegression StatisticsMultiple R0.86075031R Square0.74089109Adj R Square0.64372525Standard Error 6.0861957Observations 12Example,Problem 17.27,cont.Microsoft Excel OutputThe regression equation is:2002 The Wadsworth GroupCoefficientsStandardErrort StatP-valueIntercept75.3689846.3072930211.9494982.214E-06x11.593582890.513918773.10084590.014647x2-7.35962574.37208671-1.6833210.1308108x39.733957224.491279572.16730160.062079Example,Problem 17.27,cont.The regression equation has an adjusted R-square of 0.644.This indicates that the regression model provides a reasonable explanation for the variation in the data set.Only the coefficient for x1 is significant at the 0.05 level.One might consider removing the assembly method from the model.2002 The Wadsworth Group