STA 6127 – Fertility Example (Problem 13.17)- 3 Groups: Urban Native, Urban Migrant, Rural Migrant- Response: Fertility = # of live births by woman- Covariate: Education Level1) 1-Way ANOVA to Compare 3 Groups (Ignores Education Level)DescriptivesFERT15 4.13 1.457 .376 3.33 4.94 2 717 4.29 1.611 .391 3.47 5.12 2 720 6.00 1.777 .397 5.17 6.83 3 1052 4.90 1.829 .254 4.39 5.41 2 101.002.003.00TotalN Mean Std. Deviation Std. Error Lower Bound Upper Bound95% Confidence Interval forMeanMinimum MaximumUnadjusted means are: 4.13 (U-N), 4.29 (U-M), 6.00 (R-M)ANOVAFERT Sum ofSquares df Mean Square F Sig.Between Groups39.256 2 19.628 7.327 .002Within Groups131.263 49 2.679 Total170.519 51 Reject H0: ------------ (F(2,49)=7.327, P=.002)SSE = WSS = 131.623R2 = BSS / TSS = 39.526 / 170.519 = 0.232Multiple ComparisonsDependent Variable: FERTBonferroni-.16 .580 1.000 -1.60 1.28-1.87* .559 .005 -3.25 -.48.16 .580 1.000 -1.28 1.60-1.71* .540 .008 -3.04 -.371.87* .559 .005 .48 3.251.71* .540 .008 .37 3.04(J) GROUPNUM2.003.001.003.001.002.00(I) GROUPNUM1.002.003.00MeanDifference(I-J) Std. Error Sig. Lower Bound Upper Bound95% Confidence IntervalThe mean difference is significant at the .05 level.*. Conclude that -----------------------------------------------------------”=”-------”=”------2) Simple Linear Regression Relating Fertility to Education (Ignores Group)Model Summary.592a.351 .338 1.488Model1R R SquareAdjustedR SquareStd. Error ofthe EstimatePredictors: (Constant), EDUCa. R2 = .351ANOVAb59.806 1 59.806 27.009 .000a110.713 50 2.214170.519 51RegressionResidualTotalModel1Sum ofSquares df Mean Square F Sig.Predictors: (Constant), EDUCa. Dependent Variable: FERTb. Reject H0: -- = 0 F(1,50)=27.009, P=.000Coefficientsa6.357 .347 18.294 .000-.265 .051 -.592 -5.197 .000(Constant)EDUCModel1B Std. ErrorUnstandardizedCoefficientsBetaStandardizedCoefficientst Sig.Dependent Variable: FERTa. Fitted Equation: Fertility = 6.357 – 0.265*EDUCLinear Regression0.0 2.5 5.0 7.5 10.0educ246810fert       fert = 6.36 + -0.27 * educR-Square = 0.353) Analysis of Covariance (No Interaction Terms)Z1 = 1 for U-N, 0 ow Z2 = 1 for U-M, 0 owZ3 = 1 for R-M, 0 owCan only fit models with 2 of these variables at a time when you include intercept term!!!Variables Entered/RemovedbEDUCa. EnterZ1, Z2a. EnterModel12VariablesEnteredVariablesRemoved MethodAll requested variables entered.a. Dependent Variable: FERTb. Model Summary.592a.351 .338 1.488 .351 27.009 1 50 .000.718b.516 .486 1.311 .165 8.201 2 48 .001Model12R R SquareAdjustedR SquareStd. Error ofthe EstimateR SquareChange F Change df1 df2 Sig. F ChangeChange StatisticsPredictors: (Constant), EDUCa. Predictors: (Constant), EDUC, Z1, Z2b. Coefficientsa6.357 .347 18.294 .000 5.659 7.055-.265 .051 -.592 -5.197 .000 -.368 -.1637.160 .365 19.604 .000 6.425 7.894-.242 .045 -.540 -5.325 .000 -.333 -.150-1.641 .450 -.411 -3.648 .001 -2.546 -.737-1.402 .436 -.363 -3.213 .002 -2.279 -.525(Constant)EDUC(Constant)EDUCZ1Z2Model12B Std. ErrorUnstandardizedCoefficientsBetaStandardizedCoefficientst Sig. Lower Bound Upper Bound95% Confidence Interval for BDependent Variable: FERTa.Coefficientsa6.357 .347 18.294 .000 5.659 7.055-.265 .051 -.592 -5.197 .000 -.368 -.1635.758 .420 13.698 .000 4.913 6.603-.242 .045 -.540 -5.325 .000 -.333 -.150-.239 .465 -.060 -.515 .609 -1.174 .6951.402 .436 .377 3.213 .002 .525 2.279(Constant)EDUC(Constant)EDUCZ1Z3Model12B Std. ErrorUnstandardizedCoefficientsBetaStandardizedCoefficientst Sig. Lower Bound Upper Bound95% Confidence Interval for BDependent Variable: FERTa. 4) Analysis of Covariance (Model With Interaction)Variables Entered/RemovedbEDUCa. EnterZ1, Z2a. EnterEDUC_Z1,EDUC_Z2a. EnterModel123VariablesEnteredVariablesRemoved MethodAll requested variables entered.a. Dependent Variable: FERTb. Model Summary.592a.351 .338 1.488 .351 27.009 1 50 .000.718b.516 .486 1.311 .165 8.201 2 48 .001.719c.517 .465 1.337 .001 .065 2 46 .937Model123R R SquareAdjustedR SquareStd. Error ofthe EstimateR SquareChange F Change df1 df2 Sig. F ChangeChange StatisticsPredictors: (Constant), EDUCa. Predictors: (Constant), EDUC, Z1, Z2b. Predictors: (Constant), EDUC, Z1, Z2, EDUC_Z1, EDUC_Z2c.Coefficientsa6.357 .347 18.294 .000 5.659 7.055-.265 .051 -.592 -5.197 .000 -.368 -.1637.160 .365 19.604 .000 6.425 7.894-.242 .045 -.540 -5.325 .000 -.333 -.150-1.641 .450 -.411 -3.648 .001 -2.546 -.737-1.402 .436 -.363 -3.213 .002 -2.279 -.5257.268 .520 13.965 .000 6.220 8.315-.264 .089 -.590 -2.976 .005 -.443 -.085-1.719 .796 -.430 -2.159 .036 -3.322 -.116-1.615 .745 -.418 -2.167 .035 -3.114 -.115.017 .124 .032 .140 .890 -.232 .266.040 .113 .086 .353 .726 -.187 .267(Constant)EDUC(Constant)EDUCZ1Z2(Constant)EDUCZ1Z2EDUC_Z1EDUC_Z2Model123B Std. ErrorUnstandardizedCoefficientsBetaStandardizedCoefficientst Sig. Lower Bound Upper Bound95% Confidence Interval for BDependent Variable: FERTa.Linear Regression246810fert fert = 7.27 + -0.26 * educR-Square = 0.26rur_mig urb_migurb_nat  fert = 5.65 + -0.22 * educR-Square = 0.440.0 2.5 5.0 7.5 10.0educ246810fert    fert = 5.55 + -0.25 * educR-Square =