Refer to The Archives of Disease in Childhood (Apr. 2000) study of whether height influences a child€™s progression through elementary school, presented in Exercise. Recall that Australian schoolchildren were divided into equal thirds (tertiles) based on age (youngest third, middle third, and oldest third). The average heights of the three groups (for which all height measurements were standardized by using z-scores), by gender, are shown in the accompanying table.

a. Propose a regression model that will enable you to compare the average heights of the three age groups for boys.
b. Find the estimates of the ’s in the model you proposed in part a.
c. Repeat parts a and b for girls.

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Middle Youngest Tertile Mean Height 0.33 0.27 Tertile Mean Oldest Tertile Height Mean Height Boys Girls 0.33 0.18 0.16 0.21