Investigation 13: Speaking and intelligence (due Tues, Mar 7)

You may work with one other person on this assignment, handing in one report with both names.  Word-processed reports are preferred to hand-written ones. Please copy/paste relevant, well-labeled Minitab output into a Word file as appropriate.

Parents of children who speak at a young age like to believe that this bodes well for the child exhibiting high intelligence later in life. To investigate this possibility, researchers collected data on the age of first speaking (in months) and score on the Gesell aptitude test taken later in life for a sample of 22 children. The data can be found in the Minitab worksheet gesell.mtw.

a) Examine a scatterplot of Gesell score vs. age of first speaking. Comment on whether these two variables appear to be associated.

b) Determine the regression equation for predicting a child’s Gesell score from the age at which he/she first speaks. Report the equation, along with the value of r², and superimpose the line on the scatterplot. (Turn in this plot.)

c) Do any of the children appear to be outliers in the age variable? If so, what is the ID number for this child? How long did it take him/her to speak? Also report the residual value for this child, and comment on whether it is exceptionally large (in absolute value) compared to other residual values.

d) Remove this child from the analysis. Then reproduce a scatterplot and recalculate the regression equation and value of r². Comment on how these have changed.

e) Now remove the child who took the next longest time to speak, again look at a scatterplot, and the regression equation and value of r². Comment again on how these have changed.

f) Write a paragraph explaining (as if to someone with no formal knowledge of statistics) why the regression line and correlation change so much and also summarizing what these data reveal concerning the relationship between age of first speaking and aptitude.