Solved: Height versus Head Circumference A pediatrician wants to determine the relation

Chapter 14, Problem 13

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Height versus Head Circumference A pediatrician wants to determine the relation that may exist between a childs height and head circumference. She randomly selects 11 children from her practice, measures their heights and head circumferences, and obtains the following data: Height (inches), x Head Circumference (inches), y Height (inches), x Head Circumference (inches), y 27.75 17.5 26.5 17.3 24.5 17.1 27 17.5 25.5 17.1 26.75 17.3 26 17.3 26.75 17.5 25 16.9 27.5 17.5 27.75 17.6 Source: Denise Slucki, student at Joliet Junior College Use the results from in Section 4.2 to answer the following questions: (a) Treating height as the explanatory variable, x, determine the estimates of b0 and b1. (b) Compute the standard error of the estimate, se. (c) Determine whether the residuals are normally distributed. (d) If the residuals are normally distributed, determine sb1 . (e) If the residuals are normally distributed, test whether a linear relation exists between height and head circumference at the a = 0.01 level of significance. (f) If the residuals are normally distributed, construct a 95% confidence interval about the slope of the true least-squares regression line. (g) A child comes in for a physical, and the nurse determines his height to be 26.5 inches. However, the child is being rather uncooperative, so the nurse is unable to measure the head circumference of the child. What would be a good estimate of this childs head circumference? Why is this a good estimate?