2. The data set kyphosis is from a study on the results of corrective spinal surgery on n - 81 children. Four variables of interest were measured for each child Age-child's age in months Number-number of vertebrae involved in the surgery . Start - the topmost vertebrae operated on . Kyphosis - binary indicator of presence/absence of a kyphosis, or spinal deformation after surgery The output of a particular model fit in R is shown below. > kyp.g1m summary (kyp.glm) Call: glm(formula - Kyphosis- , family = binomial, data = kyphosis) Devian ce Residuals : 3Q Max 2.3124 -0.5484 -0.3632 -0.1659 2.1613 Min 1Q Median Coefficients: Estimate Std. Error z value Pr(> |zl) (Intercept) -2.036934 1.449575 1.405 0.15996 Number Start 0.010930 0.006446 1.696 0.08996 0.410601 0.224861 1.826 0.06785 0.206510 0.067699-3.050 0.00229** Signif. codes: 0* 0.001 ** 0.01* 0.05 . 0.11 (Dispersion parameter for binomial family taken to be 1) Null deviance: 83.234 on 80 degrees of freedom Residual deviance: 61.380 on 77degrees of freedom AIC: 69.38 Number of Fisher Scoring iterations: 5 (a) Write down the theoretical model and assumptions corresponding to model kyp.glm, clearly specifying each of the three GLM components: the random component, the svstematic component, and the link function (b) Use the printed results to find an approximate 95% confidence interval for the coefficient corresponding to Start. 2. The data set kyphosis is from a study on the results of corrective spinal surgery on n - 81 children. Four variables of interest were measured for each child Age-child's age in months Number-number of vertebrae involved in the surgery . Start - the topmost vertebrae operated on . Kyphosis - binary indicator of presence/absence of a kyphosis, or spinal deformation after surgery The output of a particular model fit in R is shown below. > kyp.g1m summary (kyp.glm) Call: glm(formula - Kyphosis- , family = binomial, data = kyphosis) Devian ce Residuals : 3Q Max 2.3124 -0.5484 -0.3632 -0.1659 2.1613 Min 1Q Median Coefficients: Estimate Std. Error z value Pr(> |zl) (Intercept) -2.036934 1.449575 1.405 0.15996 Number Start 0.010930 0.006446 1.696 0.08996 0.410601 0.224861 1.826 0.06785 0.206510 0.067699-3.050 0.00229** Signif. codes: 0* 0.001 ** 0.01* 0.05 . 0.11 (Dispersion parameter for binomial family taken to be 1) Null deviance: 83.234 on 80 degrees of freedom Residual deviance: 61.380 on 77degrees of freedom AIC: 69.38 Number of Fisher Scoring iterations: 5 (a) Write down the theoretical model and assumptions corresponding to model kyp.glm, clearly specifying each of the three GLM components: the random component, the svstematic component, and the link function (b) Use the printed results to find an approximate 95% confidence interval for the coefficient corresponding to Start
