Researchers studied the impact on children€™s future incomes due to moving to wealthier neighborhoods. For each child in the study, researchers computed the percentile of the child€™s future income (at age 24 years) for incomes between the poorer neighborhood and the wealthier neigh- borhood. So, an income at the 0th percentile is equal to the poorer neighborhood€™s median income and an income at the 100th percentile is equal to the wealthier neighbor- hood€™s median income. The future-income percentiles are shown in Table 66 for various ages when children moved. Let y the future-income percentile for a child who at age x years moved to a wealthier neighborhood.
a. Construct a scatterplot of the data.
b. Is the association positive, negative, or neither? Why does that make sense in this situation?
c. Find the linear regression equation.
d. Find the coefficient of determination. What does it mean in this situation?
e. Use the model to predict the future-income percentile for a child who at age 15 years moved to a wealthier neighborhood. Compute the residual. What does it mean in this situation?

Transcribed Image Text:

Table 66 Moving Ages versus Future-Income Percentiles Age when Moved Future-Income Percentile (years) 12 43 15 42 17 18 19 19