\fName: Data have been collected at a local maternity ward on the first 100 babies delivered at the hospital (birthdata.SAS7bdat). The following variables (maternal age, gestational age, BMI, gravidity, and birthweight) were collected on all observations. 1. Isthere a linear relationship between maternal age and birthweight? Compute the Pearson correlation with its associated 95% confidence interval between maternal age and birthweight and comment on the strength of the association. 10 points . How much variance in birthweight is explained by maternal age? 5 points . Fit a simple linear regression using BMI as a predictor of birthweight and report the equation of the best-fitted line. 10 points . Provide an appropriate interpretation for the computed intercept and the computed slope. 4 points. . What is the predicted birthweight for a baby born to a person with a BMI = 25kg/m?? 5 points . Provide an assessment of the fit of the model. 6 points . Fit a Multiple Linear Regression model to find independent risk factors of birth weight (Dependent variable). Use maternal age, gestational age, BMI, and gravidity as independent variables. Report regression coefficients with 95% confidence intervals and p-value. 10 points . Based on the regression model fitted in question 7, what can be said about birthweight, i.e., how much variance is explained by the model? 10 points . What is the predicted birthweight of a baby born at 39 weeks to a person aged 25, with a BMI of 30 kg/m2, and 4 prior pregnancies? 10 points Perform an appropriate diagnostic of the fitted model. 10 points 11. Data have been collected at a local ICU (see ICU.sas7bdat). Data collected included vital status at discharge (STA), age (AGE), cancer part of the present problem (CAN}, CPR before ICU admission (CPR), infection probable at ICU admission (INF), and race (RACE). Fit a multivariable logistic regression model to find predictors of vital status at discharge (STA). The model should include age, cancer (CAN), CPR, infection (INF), and race. Provide and interpret the 95% confidence interval for the adjusted odds ratio for each variable in the model. Report on the model's goodness-of-fit to the data. 20 points