A student in an animal physiology class did an experiment to determine the effect of environmental temperature on the heart rate of leopard frogs. She obtained 11 frogs of approximately the same age, size, and gender, and randomly assigned each animal to a container kept at a temperature between 3 and 33°C. After the frogs had equilibrated to the ambient temperature, she measured their basal heart rate (BHR). The output below displays the results of exploratory data analysis and linear regression analysis of the association between basal heart rate (RHR) and Temporoturo (T

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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Given the data provided, I need help solving parts C-E of my problem. Thank you in advance!
Cause
effect
5.
a. What is the predictor (X) variable and what is the response (Y) variable?
X-basal heart sate
Y- temperature
Do the data meet the assumptions for linear regression? Explain with reference to the
study description and specific output that support your statements.
b.
RUs v
residuals are normal
each animal randomly assigred.
Association is inear
No outliers
same size, age, gendry tomp targe
Assumptions are FuifFiled
Write the regression equation for this relationship (i.e., include the actual slope and
intercept coefficient values, and use the variable names Temp and BHR).
C.
d.
Use the regression equation to compute the predicted value for heart rate (ỳ) and the
residual for each of the sub-set of the following temperature (X) values:
Frog ID#
1
3
9.
11
Temperature
9.
15
21
27
33
BHR (beats/min)
3
14
20
28
33
42
Predicted BHR
Residual
e. The first line of the regression Coefficients: table that you generated presents
results for (Intercept), including the estimate and results of a t-test for the Null
hypothesis that the y-intercept is 0.
(1) What is the biological interpretation of (Intercept) =-0.236?
(2) Explain the meaning of the p-value from the associated t-test.
13.6
Transcribed Image Text:Cause effect 5. a. What is the predictor (X) variable and what is the response (Y) variable? X-basal heart sate Y- temperature Do the data meet the assumptions for linear regression? Explain with reference to the study description and specific output that support your statements. b. RUs v residuals are normal each animal randomly assigred. Association is inear No outliers same size, age, gendry tomp targe Assumptions are FuifFiled Write the regression equation for this relationship (i.e., include the actual slope and intercept coefficient values, and use the variable names Temp and BHR). C. d. Use the regression equation to compute the predicted value for heart rate (ỳ) and the residual for each of the sub-set of the following temperature (X) values: Frog ID# 1 3 9. 11 Temperature 9. 15 21 27 33 BHR (beats/min) 3 14 20 28 33 42 Predicted BHR Residual e. The first line of the regression Coefficients: table that you generated presents results for (Intercept), including the estimate and results of a t-test for the Null hypothesis that the y-intercept is 0. (1) What is the biological interpretation of (Intercept) =-0.236? (2) Explain the meaning of the p-value from the associated t-test. 13.6
5. A student in an animal physiology class did an experiment to determine the effect of
environmental temperature on the heart rate of leopard frogs. She obtained 11 frogs of
approximately the same age, size, and gender, and randomly assigned each animal to a
container kept at a temperature between 3 and 33°C. After the frogs had equilibrated to their
ambient temperature, she measured their basal heart rate (BHR).
The output below displays the results of exploratory data analysis and linear regression
analysis of the association between basal heart rate (BHR) and Temperature (Temp). Note
that the coefficients Intercept and Temp refer to the y-intercept and slope of the regression
equation, respectively.
Shapiro-Wilk normality test
data:
residuals (1m (BHR ~ Temp, data))
W = 0.98973, p-value = 0.9972
%3D
Residuals vs Fitted
Normal Q-Q
Residuals vs Leverage
2.
03
30
03
0.5
04
20
0.5
80
Og
Y --- Cook's distance
08
10
20
30
40
-1.5
0.5
0.5
1.5
0,00
0.10
0.20
0.30
Fitted values
Im(BHR - Temp)
Theoretical Quantiles
Im(BHR - Temp)
Leverage
Im(BHR - Temp)
Plot of BHR vs Temp
Call:
40
lm (formula = BHR ~ Temp, data = data)
Residuals:
10 Median
-3.0182 -1.0636 0.4182
Min
3Q
Маx
20
0.9818 2.8909
Coefficients:
Estimate Std. Error t value Pr(>|t|)
1.
(Intercept) -0.23636
Temp
1.17059
-0.202
0.844
5.
10
15 20 25 30
1.26061
0.05753 21.912 4.05e-09 ***
Temp
Signif. codes: 0 '***' 0.001 I*** 0.01 I*! 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.81 on 9 degrees of freedom
Multiple R-squared: 0.9816, Adjusted R-squared: 0.9796
F-statistic: 480.1 on 1 and 9 DF,
p-value: 4.053e-09
13.5
Residuals
-3 -2 -1 0 1 2 3
Standardized residuals
Standardized residuals
O L-
Transcribed Image Text:5. A student in an animal physiology class did an experiment to determine the effect of environmental temperature on the heart rate of leopard frogs. She obtained 11 frogs of approximately the same age, size, and gender, and randomly assigned each animal to a container kept at a temperature between 3 and 33°C. After the frogs had equilibrated to their ambient temperature, she measured their basal heart rate (BHR). The output below displays the results of exploratory data analysis and linear regression analysis of the association between basal heart rate (BHR) and Temperature (Temp). Note that the coefficients Intercept and Temp refer to the y-intercept and slope of the regression equation, respectively. Shapiro-Wilk normality test data: residuals (1m (BHR ~ Temp, data)) W = 0.98973, p-value = 0.9972 %3D Residuals vs Fitted Normal Q-Q Residuals vs Leverage 2. 03 30 03 0.5 04 20 0.5 80 Og Y --- Cook's distance 08 10 20 30 40 -1.5 0.5 0.5 1.5 0,00 0.10 0.20 0.30 Fitted values Im(BHR - Temp) Theoretical Quantiles Im(BHR - Temp) Leverage Im(BHR - Temp) Plot of BHR vs Temp Call: 40 lm (formula = BHR ~ Temp, data = data) Residuals: 10 Median -3.0182 -1.0636 0.4182 Min 3Q Маx 20 0.9818 2.8909 Coefficients: Estimate Std. Error t value Pr(>|t|) 1. (Intercept) -0.23636 Temp 1.17059 -0.202 0.844 5. 10 15 20 25 30 1.26061 0.05753 21.912 4.05e-09 *** Temp Signif. codes: 0 '***' 0.001 I*** 0.01 I*! 0.05 '.' 0.1 ' ' 1 Residual standard error: 1.81 on 9 degrees of freedom Multiple R-squared: 0.9816, Adjusted R-squared: 0.9796 F-statistic: 480.1 on 1 and 9 DF, p-value: 4.053e-09 13.5 Residuals -3 -2 -1 0 1 2 3 Standardized residuals Standardized residuals O L-
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