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1. (25 points) In a study on the risk of teen mothers having low birth weight babies published in 1998 in the Journal of School Health, the authors reported the following data set, where x represents maternal age (in years) and Y represents birth weight of baby (in grams). X 15 17 18 15 16 19 17 16 18 19 Y 2289 3393 3271 2648 2897 3327 2970 2535 3138 3573 a. A researcher considers a simple linear regression with a as the predictor and Y as the response. Note that, in the data, each x value corresponds to two different Y values. Why are there such differences? Explain briefly using the simple linear regression model. b. Under the simple linear regression model, the researcher considers the mean birth weights of two babies. The first baby's mother's maternal age is 17; the second baby's mother's maternal age is 16. Express the difference: E(birth weight of the first baby) - E(birth weight of the second baby) (1) in terms of the regression coefficient(s). c. Find an estimate of the difference in (1) of part b. Show your steps on how you find the answer to receive full credit. d. Find the standard error (s.e.) of the estimate in part c. Again, you need to show your calculation in order to receive full credit. e. Find a 95% confidence interval for the difference in (1). Again, you need to show your calculation in order to receive full credit