Consider the data in the dataframe phbirths available from the faraway package in R. This dataset concerns the birth weights of 1115 babies in the US state of Philadelphia in 1990. The variables recorded are: grams A baby's birth weight, in grams (the response variable). black Whether the birth mother was black (boolean). educ The number of years the birth mother had received education. smoke Whether the birth mother smoked during pregnancy (boolean). gestate A baby's gestational age at birth, in weeks. Use linear modelling and any techniques you have been taught in this course (or other tech- niques, if you want!) to model the birth weight of babies as a function of the other predictor variables in this dataset. Describe what you are doing at each stage, even if you are apply- ing automated techniques like stepwise regression. Include plots and regression output where appropriate. The aim of this exercise is not necessarily to come up with the "right" model for the data (hopefully some of you will settle on the same model as I have, but quite possibly some of you will find better models!). Rather, the aim is to demonstrate an understanding of the model-fitting process. Techniques you might consider include: interactions, polynomial terms for predictor variables, transforming the response or predictor variables, centring predictor variables, stepwise regres- sion, excluding influential observations, F-tests for model selection, diagnostic plots etc. How- ever, you do not have to use all of these ideas to get full marks. Provide an interpretation of your results. Remember, as statisticians, we often like to express our uncertainty in point-estimates. Some context specific questions you might like to consider