(i) Draw a scatter diagram between height and FEV. (ii) Find the best-fitting regression line, and test it for statistical significance using F-test and t test. (iii) Find coefficient of correlation and coefficient of determination.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
icon
Concept explainers
Question
100%
How i can solve i,ii,iii,iv,v,vi,vii,viii Please help me.
Q. 1 Forced expiratory volume (FEV) is a standard measure of pulmonary
function. To identify people with abnormal pulmonary function, standards
of FEV for normal people must be established. One problem here is that
FEV is related to both age and height. Let us focus on boys who are ages 10
-15 and postulate a regression model of the form
FEV
= a + B (height) + ɛ
Data were collected on FEV and height for 655 boys in this age group
residing in Tecumseh, Michigan. Following table presents the mean FEV in
liters for each of twelve 4-cm height groups.
S.#
Height
(cm)
134
Mean FEV
(L)
1
1.7
138
1.9
3
142
2.0
4
146
2.1
150
2.2
6.
154
2.5
7
158
2.7
8.
162
3.0
9.
166
3.1
10
170
3.4
11
174
3.8
12
178
3.9
Required:
(i) Draw a scatter diagram between height and FEV.
(ii) Find the best-fitting regression line, and test it for statistical significance
using F-test and t test.
(iii) Find coefficient of correlation and coefficient of determination.
(iv) What proportion of the variance of FEV can be explained by height?
Transcribed Image Text:Q. 1 Forced expiratory volume (FEV) is a standard measure of pulmonary function. To identify people with abnormal pulmonary function, standards of FEV for normal people must be established. One problem here is that FEV is related to both age and height. Let us focus on boys who are ages 10 -15 and postulate a regression model of the form FEV = a + B (height) + ɛ Data were collected on FEV and height for 655 boys in this age group residing in Tecumseh, Michigan. Following table presents the mean FEV in liters for each of twelve 4-cm height groups. S.# Height (cm) 134 Mean FEV (L) 1 1.7 138 1.9 3 142 2.0 4 146 2.1 150 2.2 6. 154 2.5 7 158 2.7 8. 162 3.0 9. 166 3.1 10 170 3.4 11 174 3.8 12 178 3.9 Required: (i) Draw a scatter diagram between height and FEV. (ii) Find the best-fitting regression line, and test it for statistical significance using F-test and t test. (iii) Find coefficient of correlation and coefficient of determination. (iv) What proportion of the variance of FEV can be explained by height?
(v) Provide 95% confidence intervals for the regression parameters
of the data.
(vi) A child is 12 years old and 160 cm tall and FEV is 2.5L. Can
his FEV considered abnormal for his age and height? (Hint: Find
Predictions interval from Regression Lines for Individual
Observations)
(vii) Compute the standard error and 95% confidence interval for
the average value of FEV over a large number of boys with height
of 160 cm (Hint: Find Confidence Interval for Predictions Made
from Regression Lines for the Average Value of y for a Given x).
(viii) Interpret the results.
Transcribed Image Text:(v) Provide 95% confidence intervals for the regression parameters of the data. (vi) A child is 12 years old and 160 cm tall and FEV is 2.5L. Can his FEV considered abnormal for his age and height? (Hint: Find Predictions interval from Regression Lines for Individual Observations) (vii) Compute the standard error and 95% confidence interval for the average value of FEV over a large number of boys with height of 160 cm (Hint: Find Confidence Interval for Predictions Made from Regression Lines for the Average Value of y for a Given x). (viii) Interpret the results.
Expert Solution
steps

Step by step

Solved in 6 steps with 2 images

Blurred answer
Knowledge Booster
Points, Lines and Planes
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman