The average height of a large group of children is 43 inches, and the SD is 1.2 inches. The average weight of these children is 40 pounds, and the SD is 2 pounds. The correlation between the two variables is r = 0.65. A scatter diagram is drawn, with height on the horizontal axis and weight on the vertical axis. The scatter diagram is football shaped. The regression line for predicting weight based on height is drawn through the scatter.
The average height of a large group of children is 43 inches, and the SD is 1.2
inches. The average weight of these children is 40 pounds, and the SD is 2
pounds. The
A
vertical axis. The scatter diagram is football shaped. The regression line for
predicting weight based on height is drawn through the scatter.
(a) Predict the weights and the typical size of the error for those predictions in
each of the following case:
A child who is 43 inches tall is predicted to weigh _____________ pounds, give or
take _____________ pounds.
A child who is 41.8 inches tall is predicted to weigh ____________ pounds, give or
take _____________ pounds.
37 pounds and is 41.8 inches tall. Relative to all
children with the same height, this child’s weight is (pick one)
(i) smaller than average
(ii) about average
(iii) larger than average
(iv) impossible to determine
Show your work and justify your answer.
(c) Suppose a child’s height is at the 29th percentile of all heights. Using
regression, our best guess is that the child’s weight (measured in pounds) is at the
___________________ percentile compared to all other children.
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