The data at the bottom contains the observations Francis Galton used in 1885 to estimate the relationship between the heights of parents and the heights of their children. The column Children refers to the height (in inches) of a child, and the column Mid-Parents refers to the average height (in inches) of the mother and father of that child.

a. Calculate the regression Height of Children = a +b (Height of Mid-Parents).

b. Calculate the average for Height of Children, and calculate the average Height of Mid-Parents.

c. Create a new variable in Excel which is the Height of Children measured in terms of deviations from its mean. Call this new variable y. Also, create a new variable in Excel which is the Height of Mid-Parents measured in terms of deviations from its mean. Call this new variable x. Calculate the regression y = a + bx.

d. If a person's parents are 2 inches above average height, do you predict their children to be above or below average height? And how many inches above or below average height?

e. What fraction of the variation in the heights of children is explained by the heights of their parents?

f. Show the graph of the data with the equation for your regression line from part 2a of this question.

g. Use the F statistic to test the hypothesis that there is no relation between the heights of children and the heights of their parents at the 5% level of significance. Do you reject this hypothesis or not?

h. If you reject the hypothesis in the previous question, what is the probability of a false positive result?

Data:

Mid-Parents	Children
73	72.2
73	73.2
73	73.2
73	73.2
72.5	68.2
72.5	69.2
72.5	69.2
72.5	70.2
72.5	71.2
72.5	71.2
72.5	72.2
72.5	72.2
72.5	72.2
72.5	72.2
72.5	72.2
72.5	72.2
72.5	72.2
72.5	73.2
72.5	73.2
72.5	73.7
72.5	73.7
72.5	73.7
72.5	73.7
71.5	65.2
71.5	66.2
71.5	66.2
71.5	66.2
71.5	67.2
71.5	67.2
71.5	67.2
71.5	67.2
71.5	68.2
71.5	68.2
71.5	68.2
71.5	69.2
71.5	69.2
71.5	69.2
71.5	69.2
71.5	69.2