Outliers · Exercise 21

shows the average heights for American boys in 1990.

$$\begin{array}{cc}\text{Age (years)}& \text{Height (centimeters)}\\ \text{Birth}& \text{50.8}\\ \text{2}& \text{83.8}\\ \text{3}& \text{91.4}\\ \text{5}& \text{106.6}\\ \text{7}& \text{119.3}\\ \text{10}& \text{137.1}\\ \text{14}& \text{157.5}\end{array}$$

(a) Decide which variable should be the independent variable and which should be the dependent variable.
(b) Draw a scatter plot of the data.
(c) Does it appear from inspection that there is a relationship between the variables? Why or why not?
(d) Calculate the least-squares line. Put the equation in the form ŷ = a + bx.
(e) Find the correlation coefficient. Is it significant?
(f) Find the estimated average height for a 1-year-old. Find the estimated average height for an 11-year-old.
(g) Does it appear that a line is the best way to fit the data? Why or why not?
(h) Are there any outliers in the data?
(i) Use the least-squares line to estimate the average height for a 62-year-old man. Do you think that your answer is reasonable? Why or why not?
(j) What is the slope of the least-squares (best-fit) line? Interpret the slope.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Statistics · §12.5 Outliers · Exercise 21