Consider the data in the following table.

a. First convert ages to decimal years (e.g., 1 year 6 months gives 1.5 years). Draw a scatter diagram for the variable pair vocabulary size (Y) and age (X).
b. Calculate the least-squares estimates of the parameters of the regression line. Sketch this regression line on the scatter diagram.
c. Add a new observation to the vocabulary data, with values 0.00 years and 0 words. Plot this new point. Logically, this value should be on the line of vocabulary growth. Is it near the fitted line from part (b)?
d. Re-compute the least-squares estimates of the regression line to include the (0, 0) observation (n = 16). Sketch the new line distinctly on the scatter diagram.
e. Does either fitted line describe the data pattern adequately? If not, sketch your idea of the true relationship. If the data included observations through age 30 years, what would the extrapolated curve look like?
f. The data appear to be from one child. If this is true, what assumption of the least-squares approach is most likely violated, and why?

Age Age Vocabulary Size Years Months Vocabulary Size Years Months 10