(a) Use the fitted regression Volume = 10.0655 + 86.0308 × Aroc to verify that the predicted volume is the fitted response value for x* = 0.65. Start with the coefficient results in the regression line to reduce the roundoff error. If x* = 0.65, what is the predicted mean response value µvolume? Verify that it is equivalent to the value in the table for "Predicted Volume". (Enter your answer rounded to four decimal places.) Hvolume (b) What is the 95% interval we want? (Enter your answers for the lower and upper limits of your chosen interval, rounded to three decimal places.)

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Analysis of the sample data of size n = 29 from the study of the effect of introspective ability on brain anatomy shows
that the relationship between gray-matter volume and introspective ability, as measured by Aroc, is roughly linear. We
might want to predict the mean gray-matter volume of a person with the introspective ability of 0.65. The JMP output for
prediction when x* = 0.65 is given.
StdErr
StdErr
Upper 95%
Mean Volume Mean Volume
Predicted
Lower 95%
Lower 95%
Upper 95%
Aroc Volume
Pred
Indiv
Volume
Indiv Volume Indiv Volume
Volume
Volume
|1 0.65
65.9855
1.4690
62.9714
68.9997
8.0441
49.4805
82.4906
(a) Use the fitted regression Volume = 10.0655 + 86.0308 × Aroc to verify that the predicted volume is the fitted
response value for x* = 0.65. Start with the coefficient results in the regression line to reduce the roundoff error.
If x* =
0.65, what is the predicted mean response value µvolume? Verify that it is equivalent to the value in the table for
"Predicted Volume". (Enter your answer rounded to four decimal places.)
Hvolume =
(b) What is the 95% interval we want? (Enter your answers for the lower and upper limits of your chosen interval,
rounded to three decimal places.)
Transcribed Image Text:Analysis of the sample data of size n = 29 from the study of the effect of introspective ability on brain anatomy shows that the relationship between gray-matter volume and introspective ability, as measured by Aroc, is roughly linear. We might want to predict the mean gray-matter volume of a person with the introspective ability of 0.65. The JMP output for prediction when x* = 0.65 is given. StdErr StdErr Upper 95% Mean Volume Mean Volume Predicted Lower 95% Lower 95% Upper 95% Aroc Volume Pred Indiv Volume Indiv Volume Indiv Volume Volume Volume |1 0.65 65.9855 1.4690 62.9714 68.9997 8.0441 49.4805 82.4906 (a) Use the fitted regression Volume = 10.0655 + 86.0308 × Aroc to verify that the predicted volume is the fitted response value for x* = 0.65. Start with the coefficient results in the regression line to reduce the roundoff error. If x* = 0.65, what is the predicted mean response value µvolume? Verify that it is equivalent to the value in the table for "Predicted Volume". (Enter your answer rounded to four decimal places.) Hvolume = (b) What is the 95% interval we want? (Enter your answers for the lower and upper limits of your chosen interval, rounded to three decimal places.)
(b) What is the 95% interval we want? (Enter your answers for the lower and upper limits of your chosen interval,
rounded to three decimal places.)
Lower limit =
Upper limit =
Transcribed Image Text:(b) What is the 95% interval we want? (Enter your answers for the lower and upper limits of your chosen interval, rounded to three decimal places.) Lower limit = Upper limit =
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