A pediatrician want to determine the relation 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 obtains the accompanying data. Complete parts (a) through (g).
Data table. In inches
Height, x Head Circumference, y Height, x Head Circumference, y
27.75 17.7 27 17.3
24.7 17.1 27.5 17.5
25.5 17.1 26.75 17.3
25.5 17.3 26.75 17.5
25 16.9 27.5 17.5
27.75 17.6
(a) Find the least -squares regression line treating height as the explanatory variable and head circumference as the response variable.
The least squares regression line is Y= (......) X + (......)(Round to four decimal places as needed)
(b) Interpret the slope and y-intercept, if appropriate.
(c) Use the regression equation to predict the head circumference of the child who is 25 inches tall.
(d) Compute the residual based on the observed head circumference of the 25-inch-tall child in the table. Is the head circumference of child above average or below average?
(Residual=observed y - predicted y = y- Y
(e) Draw the least squares regression line on the scatter diagram of the data and label the residual from part (d).
(f) Notice that two children are 27 inches tall. One has a head circumference 17.7 inch and other has a head circumference 17.3 inch. How can this be?
Would it be reasonable to use the least-squares regression line to predict the head circumference of a child who was 34 inches tall.