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. From their examination of the data the investigators felt that the assumptions of the linear regression model were satisfied. The computer output shown below was generated.
a) What proportion of observed variation in the surface temperature of non-vital teeth can be explained by the surface temperature of 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₎ = 0.1665. Calculate a 95% confidence interval for the true average non-vital tooth temperature when the vital tooth temperature is 30 degrees centigrade.
d) In one individual, a single surface temperature for a vital tooth is found to be 30 degrees centigrade. Use a 95% prediction interval to predict the resulting temperature of a non-vital tooth.

Question

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. From their examination of the data the investigators felt that the assumptions of the linear regression model were satisfied. The computer output shown below was generated.

a) What proportion of observed variation in the surface temperature of non-vital teeth can be explained by the surface temperature of 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₎ = 0.1665. Calculate a 95% confidence interval for the true average non-vital tooth temperature when the vital tooth temperature is 30 degrees centigrade.
d) In one individual, a single surface temperature for a vital tooth is found to be 30 degrees centigrade. Use a 95% prediction interval to predict the resulting temperature of a non-vital tooth.

Quizplus · Accepted Answer

The Answer of 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. From their examination of the data the investigators felt that the assumptions of the linear regression model were satisfied. The computer output shown below was generated. a) What proportion of observed variation in the surface temperature of non-vital teeth can be explained by the surface temperature of 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₎ = 0.1665. Calculate a 95% confidence interval for the true average non-vital tooth temperature when the vital tooth temperature is 30 degrees centigrade. d) In one individual, a single surface temperature for a vital tooth is found to be 30 degrees centigrade. Use a 95% prediction interval to predict the resulting temperature of a non-vital tooth.

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