Question

a pediatrician wants to determine the relation that exists between a childs 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). (a) find the least - squares regression line treating height as the explanatory variable and head circumference as the response variable. y = □x+□ (round the slope to three decimal places and round the constant to one decimal place as needed.) height (inches), x 27.75 24.5 25.75 26 25 27.75 26.75 27.25 26 26 27.75 head circumference (inches), y 17.4 17.0 17.1 17.5 16.8 17.6 17.3 17.4 17.2 17.5 17.5 data table

Explanation:

Step1: List data pairs

n=11; x:27.75,24.5,...,27.75; y:17.4,17.0,...,17.5

Step2: Calculate Σx, Σy

Σx=290.5, Σy=190.3

Step3: Compute Σxy, Σx²

Σxy=5027.825, Σx²=7684.625

Step4: Slope m numerator

115027.825 -290.5190.3=23.925

Step5: Slope m denominator

11*7684.625 -290.5²=140.625

Step6: Slope m

m=23.925/140.625≈0.170

Step7: Intercept b

b=(190.3 -0.170*290.5)/11≈12.8

Answer:

ŷ = 0.170x + 12.8