The paper cited in Exercise 5.69 gave a scatterplot in which x values were for anterior teeth. Consider the following representative subset of the data:

a. Calculate the predicted values and residuals.

b. Use the results of Part (a) to obtain SSResid and r².

c. Does the least-squares line appear to give accurate predictions? Explain your reasoning.

Data from Exercises 69

The paper “Root Dentine Transparency: Age Determination of Human Teeth Using Computerized Densitometric Analysis” (American Journal of Physical Anthropology [1991]: 25–30) reported on an investigation of methods for age determination based on tooth characteristics. With y = age (in years) and x = percentage of root with transparent dentine, a regression analysis for premolars gave n = 36, SSResid = 5987.16, and SSTo = 17,409.60. Calculate and interpret the values of r² and s_e.

Transcribed Image Text:

X y X y 15 23 44 60 2 x = 404 19 52 47 78 31 65 a = 32.080888 48 59 Σ xy = 18,448 39 55 b = 0.554929 55 61 Σ y = 545 41 32 65 60