Question: Ten individuals were recruited to participate in a study investigating if age can be predicted from the percentage of a tooth’s root with transparent dentine. The resulting data, from the anterior teeth for each individual, are summarized in the following table and scatterplot.

Participant

a. Use R software to calculate the Pearson correlation coefficient between percent of root with transparent dentine and age. Interpret this correlation in one sentence.

b. Write down the formula for an appropriate simple linear regression model for this problem and include a brief description of all model parameters and variables

in your formula in this problem’s context.

c. List the assumptions that should be checked to confirm the appropriateness of the regression model in (b) for these data. (Note: you do not actually need to check the assumptions here).

d. Using R software, fit the appropriate simple linear regression model to these data (i.e., determine the equation for the estimated regression line using these data). Write out the resulting fitted model. Is the estimate for β1 positive, and, if so, why; refer to the graph and your answer from (a) in helping to support answer this question.

e. Using R software, construct a 90% confidence interval for β1. Provide a brief interpretation of your interval.