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.
- Interpret the value of the estimated slope b = 6.
- What does the y-intercept, a=80, represent? Does this make sense? Why or why not?
- 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)
- 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.
- Does the answer in part d make sense? In your own words, explain the statement "correlation does not imply causation" in this particular example.