Friesen and Shine (2019) wanted to determine whether male Australian cane toads have different testes sizes in different parts of the species' range (edge of the range vs. core of the range). As part of the study, they needed to quantify how big a toad's testes are relative to the toad's body size. They decided to perform a linear regression of total testes mass (in mg) against body mass (in g) and use the residual for each toad as a measure of the toad's relative testes size. The Coefficient Estimates table for their least-squares regression procedure is shown below. Term Coefficient Standard Error t-value Pr > t (Intercept) 19.192 43.082 0.44547 0.65643 body mass 3.0063 0.36387 8.262 1.5733e-14 (a) Suppose the researchers do a t-test for the slope of the linear model. Write the null hypothesis for the test and show that, under the null hypothesis, the observed value of the t-statistic is indeed 8.262. (That is, do the appropriate computations to prove the value is 8.262) (b) The regression output was based on a sample of 213 cane toads. How many degrees of freedom does the appropriate t-distribution used to get the p-value and the t* critical value for confidence intervals have? (c) One toad in the dataset had a body mass of 128g and a total testes mass of 163 mg. Compute the residual corresponding to this toad and write a sentence interpreting the residual
Friesen and Shine (2019) wanted to determine whether male Australian cane toads have different testes sizes in different parts of the species' range (edge of the range vs. core of the range). As part of the study, they needed to quantify how big a toad's testes are relative to the toad's body size. They decided to perform a linear regression of total testes mass (in mg) against body mass (in g) and use the residual for each toad as a measure of the toad's relative testes size. The Coefficient Estimates table for their least-squares regression procedure is shown below. Term Coefficient Standard Error t-value Pr > t (Intercept) 19.192 43.082 0.44547 0.65643 body mass 3.0063 0.36387 8.262 1.5733e-14 (a) Suppose the researchers do a t-test for the slope of the linear model. Write the null hypothesis for the test and show that, under the null hypothesis, the observed value of the t-statistic is indeed 8.262. (That is, do the appropriate computations to prove the value is 8.262) (b) The regression output was based on a sample of 213 cane toads. How many degrees of freedom does the appropriate t-distribution used to get the p-value and the t* critical value for confidence intervals have? (c) One toad in the dataset had a body mass of 128g and a total testes mass of 163 mg. Compute the residual corresponding to this toad and write a sentence interpreting the residual
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Question
Transcribed Image Text:Friesen and Shine (2019) wanted to determine whether male Australian cane toads
have different testes sizes in different parts of the species' range (edge of the range vs. core of the range).
As part of the study, they needed to quantify how big a toad's testes are relative to the toad's body size.
They decided to perform a linear regression of total testes mass (in mg) against body mass (in g) and use
the residual for each toad as a measure of the toad's relative testes size. The Coefficient Estimates table
for their least-squares regression procedure is shown below.
Term
Coefficient
Standard Error
t-value
Pr > |t|
(Intercept)
19.192
43.082
0.44547
0.65643
body mass
3.0063
0.36387
8.262
1.5733e-1
(a) Suppose the researchers do a t-test for the slope of the linear model. Write the null hypothesis for the
test and show that, under the null hypothesis, the observed value of the t-statistic is indeed 8.262.
(That is, do the appropriate computations to prove the value is 8.262)
(b) The regression output was based on a sample of 213 cane toads. How many degrees of freedom does
the appropriate t-distribution used to get the p-value and the t* critical value for confidence intervals
have?
(c) One toad in the dataset had a body mass of 128g and a total testes mass of 163 mg. Compute the
residual corresponding to this toad and write a sentence interpreting the residual
(d) Using a t* critical value of 2.599, compute a 99% confidence interval for the slope of the population
model. Write a sentence to interpret the interval (extra space provided on next page)
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