In a Study of the Surface Temperatures of Vital (Living)

Essay

In a study of the surface temperatures of vital (living) and non-vital (dead) teeth in a random sample of 32 adults seeking dental care at a university clinic, temperatures of vital and non-vital teeth were measured for each individual. The computer output shown below was generated. ​
a) What proportion of observed variation in the surface temperature of vital teeth can be explained by the surface temperature of non-vital teeth?
b) Does the simple linear regression model appear to be useful? Justify your response with specific references to the computer output.
c) The estimated standard deviation of a + bx* for x* = 30 is calculated as: sa_+b(30) = 0.2417. Calculate a 95% confidence interval for the true average vital tooth temperature when the non-vital tooth temperature is 30 degrees centigrade.
d) In one individual, a single surface temperature for a non-vital tooth is found to be 30 degrees centigrade. Use a 95% prediction interval to predict the resulting temperature of a vital tooth.