A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 5 children and measures their height and head circumference. The data are summarized below. A normal probability plot suggests that the residuals are normally distributed. Height (inches), x 26.75 25 27.75 27 25.5
Head Circumference (inches), y 17.3 16.9 17.6 17.5 17.1
A) Treating height as the explanatory variable, x, use technology to determine the estimates of β0 and β1.
B) Use technology to compute the standard error of the estimate, s ese.
C) A normal probability plot suggests that the residuals are normally distributed. Use technology to determine sb1.
D) A normal probability plot suggests that the residuals are normally distributed. Test whether a linear relation exists between height and head circumference at α = 0.01 level of significance. State the null and alternative hypotheses for this test. Determine the P-value for this hypothesis test. What is the conclusion that can be drawn?
E) Use technology to construct a 95% confidence interval about the slope of the true least-squares regression line. What is the lower bound and upper bound?
F) Suppose a child has a height of 26.5 inches. What would be a good guess for the child's head? circumference?