4. The Classification variable gives the disease status of each individual (0: healthy controls; 1: cancer patients). Consider a logistic regression model with Classification being the response variable Y and Glucose being the explanatory variable X. That is, P(vi = 13) log p(y; = Oz;) = 80+ Pitin where yi is the value of Classification and xi is the value of Glucose for the ith individual. a. If 80 + 31xi = 3, what would be the value of P(yi = 1/xi)? (Hint: You can find the formula in the lecture slides.) i. b. Use gim to fit the above model. Attach your code and report the estimates for BO, B1 i. 5. Consider variables Glucose, Insulin and HOMA, for which the correlation matrix is given by ## Glucose Insulin HOMA ## Glucose 1.0000000 0.5046531 0.6962118 ## Insulin 0.5046531 1.0000000 0.9321978 ## HOMA 0. 6962118 0.9321978 1.0000000 a. If we perform a simple linear regression using Insulin as the response and Glucose as the predictor, would the estimated slope be positive or negative? b. After standardization, we can perform PCA (principal component analysis) using the 3 variables and get a new variable PC1 (first principal component). Below are the weights of the 3 variables used in calculating PC1. # # Glucose Insulin HOMA ## 0. 5106139 0. 5869824 0.6282716 A boxplot of PC1 against Classification (denoted by "group" in the plot) is shown on the next page. We can see that patients tend to have a larger value of PC1. Based on the given information (correlation matrix, weights