The peak flow rate of a person is the fastest rate at which the person can expel air after taking a deep breath. Peak flow rate is measured in units of liters per minute and gives an indication of the person's respiratory health. Researchers measured peak flow rate and height for each of a sample of 17 men. The results are given in the table. a. b. C. d. e. g. h. A tall? Subject 1 2 3 4 5 6 7 8 9 -1 10 11 12 13 14 15 16 17 Mean SD Height X (cm) Peak flow rate Y (l/min) 174 733 183 572 176 500 169 183 186 178] 175 172 179 171 184 200 195 176 176 190 180.4118 8.5591 738 616 787 866 670 550 660 575 577 783 625 470 642 856 660.0000 117.9952 1 If we were to predict the peak flow rate using height with a least-squares regression model, what is the slope estimate b? Create a scatterplot displaying the relationship between peak flow rate and height. Calculate the sample correlation coefficient for peak flow rate and height. Continuing with part a, what is the intercept estimate â? Based on the regression model, what is the predicted peak flow rate for a subject that is 175cm f. Looking at the original data, subject 8 is 175cm tall with a peak flow rate of 6701/min. What is the residual for this subject? Fit the least-squares model in R. What is the coefficient of determination (R²)? Using your R output, is the slope parameter significant? Report the p-value and conclude at an a = 0.05 level.
The peak flow rate of a person is the fastest rate at which the person can expel air after taking a deep breath. Peak flow rate is measured in units of liters per minute and gives an indication of the person's respiratory health. Researchers measured peak flow rate and height for each of a sample of 17 men. The results are given in the table. a. b. C. d. e. g. h. A tall? Subject 1 2 3 4 5 6 7 8 9 -1 10 11 12 13 14 15 16 17 Mean SD Height X (cm) Peak flow rate Y (l/min) 174 733 183 572 176 500 169 183 186 178] 175 172 179 171 184 200 195 176 176 190 180.4118 8.5591 738 616 787 866 670 550 660 575 577 783 625 470 642 856 660.0000 117.9952 1 If we were to predict the peak flow rate using height with a least-squares regression model, what is the slope estimate b? Create a scatterplot displaying the relationship between peak flow rate and height. Calculate the sample correlation coefficient for peak flow rate and height. Continuing with part a, what is the intercept estimate â? Based on the regression model, what is the predicted peak flow rate for a subject that is 175cm f. Looking at the original data, subject 8 is 175cm tall with a peak flow rate of 6701/min. What is the residual for this subject? Fit the least-squares model in R. What is the coefficient of determination (R²)? Using your R output, is the slope parameter significant? Report the p-value and conclude at an a = 0.05 level.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter7: Integration
Section7.CR: Chapter 7 Review
Problem 88CR
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Transcribed Image Text:The peak flow rate of a person is the fastest rate at which the person can expel air after taking a deep breath.
Peak flow rate is measured in units of liters per minute and gives an indication of the person's respiratory
health. Researchers measured peak flow rate and height for each of a sample of 17 men. The results are given
in the table.
a.
b.
d.
e.
tall?
Subject
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Mean
SD
Create a scatterplot displaying the relationship between peak flow rate and height.
Calculate the sample correlation coefficient for peak flow rate and height.
C.
If we were to predict the peak flow rate using height with a least-squares regression model, what
is the slope estimate b?
-1
Height X (cm) Peak flow rate Y (l/min)
174
733
183
572
176
500
169
738
616
787
866
670
g.
h. (
183
186
178
175
172
179
171
184
200
195
176
176
190
180.4118
8.5591
550
660
575
577
783
625
470
642
856
660.0000
117.9952
Continuing with part a, what is the intercept estimate â?
Based on the regression model, what is the predicted peak flow rate for a subject that is 175cm
f.
Looking at the original data, subject 8 is 175cm tall with a peak flow rate of 6701/min. What is
the residual for this subject?
Fit the least-squares model in R. What is the coefficient of determination (R²)?
› Using your R output, is the slope parameter significant? Report the p-value and conclude at an
a = 0.05 level.
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Step 1: Given Information
VIEWStep 2: Plot the scattergraph
VIEWStep 3: Compute the correlation coefficient
VIEWStep 4: Determine the least square estimate of slope coefficient.
VIEWStep 5: Determine the least square estimate of intercept coefficient.
VIEWStep 6: Determine the predicted value for Y
VIEWStep 7: Compute the residual value
VIEWStep 8: Determine the coefficient of determination value
VIEWStep 9: Test the significance of the slope term
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