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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 = 87.60+0.52x. Height of father, X Height of son, y (in centimeters (in centimeters) 82.0 177.6 185.1 186.8 210- 170.7 182.4 200- 175.5 176.5 161. 171.0 190 200.5 189.2 180 161.0 166.0 155.6 173.1 170- 173.8 178. 160 187.1 175.9 189.7 195.0 130- 190.2 188.2 80.1 189.7 150 160 170 130 190 200 210 72.5 171.4 94.1 189.4 Figure 1 Send data to Excel Answer the following: 1. Fill in the blank: For these data, heights of fathers that are less than the mean of the heights of fathers tend to be paired with heights Choose one v of sons that are the mean of the heights of sons. 2. Fill in the blank: According to the regression equation, for an increase of one centimeter in father's height, there is a corresponding Choose one v of 0.52 centimeters in son's height. 3. What was the observed son's height (in centimeters) when the height of the father was 161.0 centimeters? 0 4. From the regression equation, what is the predicted son's height (in centimeters) when the height of the father is 161.0 centimeters? 0 Round your answer to at least one decimal place.)