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. Height (ст) S.# Mean FEV (L) 1 134 1.7 2 138 1.9 3 142 2.0 2.1 2.2 4 146 150 6. 154 2.5 7 158 2.7 162 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?

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. Height (ст) S.# Mean FEV (L) 1 134 1.7 2 138 1.9 3 142 2.0 2.1 2.2 4 146 150 6. 154 2.5 7 158 2.7 162 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?

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How i can solve (iii,iv)

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.
Height
(ст)
134
S.#
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.

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