Sir Francis Galton, in the late 1800s, was the first to introduce the statistical concepts of regression and correlation. He studied the relationships between pairs of variables such as the size of parents and the size of their offspring. Data similar to that which he studied are given below, with the variable x denoting the height (in centimeters) of a human father and the variable y denoting the height at maturity (in centimeters) of the father's oldest (adult) son. The data are given in tabular form and also displayed in the Figure 1 scatter plot, which gives the least-squares regression line as well. The equation for this line is =y+88.570.52x

.

Height of father, x
(in centimeters)Height of son, y
(in centimeters)
160.6170.6
181.9179.2
190.0195.4
175.1179.5
162.4167.9
201.7190.5
184.5189.0
157.2174.9
173.8170.7
182.0188.3
172.4182.3
200.4190.7
193.6188.9
176.7174.5
190.1188.7
187.9176.2
x

150

160

170

180

190

200

210

y

150

160

170

180

190

200

210

0

Figure 1
Answer the following:

1. Fill in the blank: For these data, heights of sons that are greater than the mean of the heights of sons tend to be paired with heights of fathers that are the mean of the heights of fathers. Choose onegreater thanless than
2. According to the regression equation, for an increase of one centimeter in father's height, there is a corresponding increase of how many centimeters in son's height?
3. From the regression equation, what is the predicted son's height (in centimeters) when the height of the father is 187.9 centimeters? (Round your answer to at least one decimal place.)
4. What was the observed son's height (in centimeters) when the height of the father was 187.9 centimeters?