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. (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. (b) One of the children weighs 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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 15PPS

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Related questions

Question

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.

(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.

(b) One of the children weighs 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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