Sir Francis Galton planted seeds with seven different diameters (in hundredths of an inch) and computed the average diameter of 100 seeds of their offspring [17]:

After deciding which is the dependent variable, use least squares to estimate the regression equation Y = α + βX + ε. Is there a statistically significant relationship at the 1 percent level? Plot these data in a scatter diagram with each axis going from 0 to 25 and draw in the least squares line. What would the line look like if the diameters did not regress toward the mean?

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16 17 18 19 15.3 16.0 15.6 16.3 16.0 Parent Offspring 15 270 17.3 21 17.5