A pediatrician wants to determine the relationship that exists between a
child’s height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and conducts the least-squares regression analysis with the simple linear model using StatCrunch. The output is given below:
(a) Write down the equation of the least-squares regression line treating height as the explanatory variable and head circumference as the response variable.
(b) Interpret the slope and y-intercept, if appropriate.
(c) Use the regression equation to predict the head circumference of a child who is 25 inches tall. Assume that the regression model is applicable.
(d) It is observed that one child who is 25 inches tall has a head circumference of 17.5 inches. Is the observed value above or below average among all children with heights of 25 inches?
Extracted text: Simple linear regression results: Dependent Variable: Head Circumference (inches), y Independent Variable: Height (inches), x Head Circumference (inches), y = 12.493169 + 0.18273245 Height (inches), x Sample size: 11 R (correlation coefficient) 0.91107273 R-sq 0.83005352 Estimate of error standard deviation: 0.095384195