The growth of children from early childhood through adolescence generally follows a linear pattern. Data on the heights of female Americans during childhood, from four to nine years old, were compiled and the least squares regression line was obtained as y = 80 + 6x, where y is height in centimeters and x is age in years. Note that 1 inch is equal to 2.54 centimeters.

1. Interpret the value of the estimated slope b = 6.
2. What does the y-intercept, a=80, represent? Does this make sense? Why or why not?
3. What would you predict the height to be for a female American at 8 years old? Give your answer first in centimeters then in inches. (Hint: 1 in = 2.54 cm)
4. Pick a number between 15 and 27. What would you predict the height to be for a female American at this age? Give your answer first in centimeters then in inches.
5. Does the answer in part d make sense? In your own words, explain the statement correlation does not imply causation in this particular example.