(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.)

(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.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

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 =

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