Objective Find the Coefficient of Determination and be able to interpret it. Be able to read and use computer printouts to do regression.

Transcription

1 Section 3.C Objective Find the Coefficient of Detemination and be able to intepet it. Be able to ead and use compute pintouts to do egession. Relevance To be able to find a model to best epesent quantitative data with vaiables and use it to make pedictions. Using the Calculato The egession line can be found using the calculato Put the data in L1 and L. Pess Stat Calc- #8 (o 4) Vas, Y-Vas, Function, Y1, Ente (This puts the equation into Y1) To get the coelation coefficient and coefficient of detemination to show Pess nd catalog (0) Pess D Go to Diagnostic on pess ente until you see done Using the Calculato You can see a pictue of the esidual plot using you calculato. Go to nd y= and open the scatte plot. Change the Ylistto RESID Pess Zoom 9 Resids: nd Stat The following table lists the total weight lifted by the winnes in eight weight classes of the 1996 Women s National Weightlifting Championship Weight Class (kg) Total Lifted (kg) Find LSRL... Find the coelation coefficient.. 3. Find the esidual fo a 64 kg weight class Check out the esidual plot. 1

2 Residual Plot Good Linea Residual Plot. No Patten! Intepet s (St. Deviation of Residuals) Fom a esidual plot of body weight and backpack weight, a egession finds s =.7. Intepet this value in context. The aveage eo (esidual) in pedicting the backpack weight is.7 using the leastsquaes egession line. Residual Plot: a gaphical tool fo evaluating how well a egession line fits the data. Standad Deviation of Residuals, s: a numeical estimate of the aveage size of ou pediction eos fom the egession line. Thee is anothe numeical value that tells us how well the least-squaes line pedicts values of the y Coefficient of Detemination If a line is appopiate, then we need to assess the accuacy of pedictions based on the least squaes line. It s the measue of the popotion of vaiability in the vaiable that can be explained by a linea elationship between the vaiables x and y. The vaiation in the esiduals is the key to assessing how well the model fits.

3 Coefficient of Detemination The vaiation in the esiduals is the key to assessing how well the model fits. Example # miles Cost Rental Cost = (Miles) This elationship explains 100% of the vaiation in Cost. But the line doesn t always account fo all of the vaiability. Height Shoe Size Shoe = ( height) This doesn t! Total Sum of Squaes Measues the total vaiation in the y-values. It s the sum of squaes of vetical distances Sum of the Squaes of the Total vaiation in y Find the : Height Shoe Size Don t foget to un Stat Calc -Vaiable Stats 1 st! Find the : Height Shoe Size This measues the total vaiation in y. 3

4 Sum of Squaed Eos o o SSR This is the sum of the squaed esiduals Total of the unexplained eo in the esiduals Fomula: Sum of the Squaes of the Residual ( y ŷ) o SSesid o SSR = Find the : 1 1 Height Shoe Size Don t foget to put the LSRL equation into Y1 fist. Y1: Vas Y-Vas Function Y1 Find the : Height Shoe Size E Pecent of unexplained eo: The atio / tells us what popotion of the total vaiation in y still emains afte using the egession line to pedict the value the esponse vaiable. o SS esid Coefficient of Detemination It s the pecent of vaiation in the y-vaiable (esponse) that can be explained by the least-squaes egession line of y on x. Fo height and shoe size find and intepet the coefficient of detemination. Fomula: =1 1 4

5 Fo height and shoe size find and intepet the coefficient of detemination Appoximately 83% of the vaiation in shoe size can be explained by the linea elationship between height and shoe size. Find the Coefficient of Detemination: Team Batting Avg. Mean # uns pe game Intepet this in context 59.5% of the obseved vaiability in mean numbe of uns pe game can be explained by an appoximate linea elationship between Team Batting aveage and mean uns pe game. Anothe example: If = 0.8, then what % can be explained by the least squaes egession line? = 0.8 = 64% = 0.64 Anothe example: A ecent study discoveed that the coelation between the age at which an infant fist speaks and the child s scoe on an IQ test given upon enteing school is A scatteplot of the data shows a linea fom. Which of the following statements about this is tue? A. Infants who speak at vey ealy ages will have highe IQ scoes by the beginning of elementay school than those who begin to speak late. B. 68% of the vaiation in IQ test scoes is explained by the leastsquaes egession of age at fist spoken wod and IQ scoe. C. Encouaging infants to speak befoe they ae eady can have a detimental effect late in life, as evidenced by thei lowe IQ scoes. D. Thee is a modeately stong, negative linea elationship between age at fist spoken wod and late IQ test scoe fo the individuals this study. Homewok Page 19 (49, 51, 54, 56, 58, 71-78) 5