A health researcher recently investigated the relationship between balance and bone density. A random sample of 25-year-old white women was obtained. Each woman took a standing balance test in which...

A health researcher recently investigated the relationship between balance and bone density. A random sample of 25-year-old white women was obtained. Each woman took a standing balance test in which she held her arms out horizontally and balanced on one foot. The length of time (x, in seconds) each person remained in that position was recorded. The bone density (y, in mg/cm2 ) for each person was measured using the DEXA (dual-energy X-ray absorptiometry) technique. The data are given in the following table.

a. Find the estimated regression line, and compute the residuals.

b. Carefully sketch a normal probability plot of the residuals and a plot of the residuals versus the predictor variable.

c. Do these graphs provide any evidence that the simple linear regression assumptions are invalid? Justify your answer.