The scientist Francis Galton, an early developer of regression methodology, used “midparent height,” the average of the father’s and mother’s heights, in order to predict children’s heights. Here are the heights of 11 female students along with their midparent heights in inches:

a. Construct a scatterplot of daughter’s height against the midparent height and comment on the strength of the relationship.
b. Is the daughter’s height completely and uniquely determined by the midparent height? Explain.
c. Use the accompanying Minitab output to obtain the equation of the least squares line for predicting daughter height from midparent height, and then predict the height of a daughter whose midparent height is 70 in. Would you feel comfortable using the least squares line to predict daughter height when midparent height is 74 in.? Explain.

d. What are the values of SSE, SST, and the coefficient of determination? How well does the midparent height account for the variation in daughter height?

Transcribed Image Text:

Midparent 66.0 65.5 71.5 68.0 70.0 65.5 Daughter 64.0 63.0 69.0 69.0 69.0 65.0 Midparent 67.0 70.5 69.5 64.5 Daughter 63.0 68.5 69.0 67.5 64.0 67.0