The scatterplot in Fig. 28 compares the sizes of peoples heads with the weights of their brains.

Question:

The scatterplot in Fig. 28 compares the sizes of people€™s heads with the weights of their brains.

Let h be the size (in cubic centimeters) of a person€™s head, and let w be the weight (in grams) of the person€™s brain.
a. Describe the four characteristics of the association.
b. A reasonable model is w = 0.26h + 335.43. Solve the equation for h.
c. Use the equation you found in part (b) to predict the head size of a person whose brain weighs 1142 grams. Find the error in this prediction for the person represented by the red dot in the scatterplot.
d. Predict the head sizes of people whose brains weigh 1100, 1200, 1300, 1400, and 1500, all in grams.
e. The researchers measured the heads and brains of people who had died at the Middlesex Hospital in London. A large proportion of the patients had died of cancer and the rest had died from accidents. Although the researchers found that subjects who had died from cancer had smaller brain-weight to head-size ratios than subjects who had died from accidents, the difference was small. Explain why it is important that the researchers compared the ratios if the model w = 0.26h + 335.43 was intended to be used to predict the brain weights of healthy people.