1.Lutein, an important carotenoid in the maintenance of ocular health, has been found post-mortem in the macula of eyes. Hence, a study is planned to supplement patients with high doses of lutein in capsule form to possibly prevent age-related macular degeneration, an important eye disease that can cause partial or total blindness in large numbers of older adults. To assess compliance in study participants, a blood sample will be drawn. It is estimated that a serum lutein > 5 g/dL would indicate that a participant is taking study medication. The study began in 2015. A sample of 9 participants had their lutein level measurement in 2015 and again in 2019. The researchers found a calibration error in the 2015 assays but the 2019 assays were correct. Assume that serum-lutein levels are normally-distributed. The data are shown in the table below. Use these data to answer the questions below the table.

a.Show an appropriate plot of the data to visually assess the linear relationship between serum-lutein levels for the two time points. Comment on the nature and strength of the linear relationship between the two variables.

b.Using regression methods, find the regression equation that can be used to predict the 2019 serum-lutein values from the 2015 value. Provide the regression equation that you obtain.

c.Use two statistics from the regression output to determine whether the regression equation is a good predictive equation. Explain.

d.Suppose a participant had a 2015 serum-lutein value of 5.0 g/dL. What is that person's predicted serum-lutein level based on the 2019 assay? What would the 2019 assay value be for a 2015 serum-lutein value of 8.0?

e.What is the Pearson's correlation coefficient expressing the (linear) relationship between the 2015 and 2019 serum-lutein levels? What can you conclude about the relationship between serum-lutein levels at these two time points?

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