Intercept age<50 Estimate 1.0609 Std. Error z value Pr(>|z|) 0.3867 2.74 0.0061 -2.0989 0.4788 -4.38 0.0000 Null deviance: 136.66 Residual deviance: 114.61 c1) Write the statistical model corresponding to such output. c2) Write the interpretation of the slope coefficient. Exercise 2 The data contained in the chdage dataset represent the measurements on 100 patients of two variables: the age expressed in years (AGE) and a binary variable (CHD) which assumes value 1 if the individual has a coronary heart disease and 0 otherwise. a) To investigate whether there is a relationship between the probability of having a coronary heard disease and the age of the individuals, a researcher fitted a generalized linear model (using the canonical link function) that produced the following output: Intercept age Estimate -5.3095 0.1109 Std. Error z value Pr(>|z|) 1.1337 -4.68 0.0241 4.610 0.0000 0.0000 Null deviance: Residual deviance: 136.66 107.35 al) Write the statistical model corresponding to such output (assumptions and model specification). a2) Write the interpretation of the coefficient associated with the age variable. a3) Write the system of hypotheses and perform a test to compare the fitted model with a model that includes only the intercept. Comment the result. b) The researcher then wonders whether the age might have a quadratic effect and adds the corresponding covariate to the model. The fitted model produced the following output: Estimate Std. Error z value Pr(>|z|) Intercept ? 4.2901 -0.99 0.3229 age ? 0.1947 0.315 0.7527 age2 0.0005 0.0021 ? ? Null deviance: 136.66 Residual deviance: 107.29 b1) Write the statistical model corresponding to such output. b2) Complete the missing values in the table. b3) Write the system of hypotheses and perform a test to compare the fitted model with a model that includes only the intercept. Comment the result. b4) Write the system of hypotheses and perform a test to evaluate which model is prefer- able between model (a) and (b). Comment the result. c) To further investigate the relationship between the age and the presence of heart disease, the age variable was then transformed into a dummy variable. Specifically, the new variable age<50 takes value 1 if age is smaller than 50 and 0 otherwise. With this new variable, the following output is produced when fitting the model: