Answer Happy

R code & output of 5A > fit <- glm(yºx1+x2+x3, data = data, family = 'poisson') > summary(fit) Call: glm(formula = y + x1 + x2 + x3, family = "poisson", data = data) Deviance Residuals: Min 10 Median -3.6175 -2.2930 -0.6846 30 Max 0.4949 5.8753 Coefficients: Estimate Std. Error z value Pr(>21) (Intercept) 1.462178 0.345636 4.230 2.33e-05 *** x 1 -0.259784 0.198999 -1.305 0.1917 x2 0.002247 0.006321 0.356 0.7222 x3 0.068001 0.041020 1.658 0.0974. (Dispersion parameter for poisson family taken to be 1) Null deviance: 137.24 on 24 degrees of freedom Residual deviance: 131.42 on 21 degrees of freedom AIC: 216.26 Number of Fisher Scoring iterations: 5 > fiti <- gim(yºx1+x3, data = data, family = 'poisson') > lrtest (fiti, fit) Likelihood ratio test Model 1: y - x1 + x3 Model 2: y x1 + x2 + x3 #Df LogLik Df Chisq Pr(>Chisq) 1 3 -104.19
2 4 -104.13 1 0.1267 0.7219 > lrtest (fit2, fit) Likelihood ratio test Model 1: y x1 + x2 Model 2: y - x1 + x2 + x3 #Df LogLik Df Chisq Pr(>Chisq) 1 3 -105.49 2 4 -104.13 1 2.7271 0.09866 The following critical values may be used for the questions: Xổ.05,1 = 3.841, Xổ 1,1 = 2.705, xổ 1,20 = 28.412, xổ 1,21 = 29.615, xổ 05,20 = 31.410, Xổ.05,21 32.670
5.1) Write down the canonical link of Poisson regression. [1 marks] 5.2) When all factors are considered as the explanatory variables, fit a Poison regression model for the data. [2 marks] 5.3) When the model is true and the sample size is large, what's the distribution of deviance? Conducting the goodness of fit test, show whether the model is good or not? (5 marks] 5.4) Use likelihood ratio test to test the significance of effect age (22) at level a = 0.1. (5 marks]