The Children€™s Bureau of the U.S. Department of Health and Human Services has a monu monumental job. In 2006, 510,000 children were in foster care. Of those, approximately 303,000 entered during the 2006 year (10/1/05€“9/20/06). The following table lists the ages of children who entered foster care during the 2006 year and the number in each age group.

a. Construct a scatter diagram of the ages when children entered foster care, x, and the number of children in each age group, y.
b. What do you think causes the unusual pattern shown on the scatter diagram?
c. Does it appear that these two variables are correlated?
d. Are we justified in using the techniques of linear regression on these data? Explain.
e. Are there any particular age groups where techniques of linear regression may be justified?

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Age Nmb Age NmbAge Number 47,536 20,646 18,234 16,145 10 14,919 14,159 13,196 12,380 11,312 14 15 21,062 12,829 702 154 10496 10,136 10,316 11,910 14,944 20 17 18 19 12 13