3. (6 marks) For this question we will use the same dataset as in Question 2, on low birth weight infants. (a) (Not marked.) Print out your fitted linear regression again, from part (b) of Question 2. (The reason for printing this again is that a different TA will markthis question. Therefore, they need to be able to see what your regression looked like.) (b) Using R, obtain an estimate of the mean weight of infants that are 33 cm long. Also, provide a 95% CI for this estimate. (c) By hand, estimate the mean weight of infants that are 34 cm long. Show your work. You can use the coefficient estimates that you printed in part (a). (d) Using R, obtain a prediction of the weight of a single infant that is 33 cm long. Also, provide a 95% PI for this estimate. (e) Compare the prediction you obtained in part (d) to the estimate of the mean you obtained in part (b). How do they compare? How do the intervals compare? (f) Use R. to create a plot of residuals vs. fitted values. Explain what you see, and how it relates to the model assumptions