Outliers · Exercise 19

shows the average heights for American boys in a specific year.

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

(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 of: ŷ = a + bx
(e) Find the correlation coefficient. Is it significant?
(f) Find the estimated average height for a one-year-old. Find the estimated average height for an eleven-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 sixty-two-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, Introductory Statistics 2e · §12.6 Outliers · Exercise 19