Predictor Coef Stdev. t-ratio Constant 0.12049 0.09269 1.30 0.215 Perch 0.008569 0.002456 3.49 0.004 * - 0.1886 R-Sq 46.5% R-Sq(adj) 42.7% %3D et. 3. What is the value of SE,? Interpret this value 4. Find the critical value for a 90% confidence interval for the slope of the true regression line. Then calculate and interpret the confidence interval 5. Based on the interval, is there convincing evidence of a linear association between number of perch and percent killed? Explain

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Here is one way in which nature regulates the size of animal populations: high population dehslty
attracts predators, which remove a higher proportion of the population than when the density of the
prey is low. One study looked at kelp perch and their common predator, the kelp bass. On each of four
occasions, the researcher set up four large circular pens on sandy ocean bottoms off the coast of
southern California. He randomly assigned young perch to 1 of 4 pens so that one pen had 10 perch,
one pen had 20 perch, one pen had 40 perch and the final pen had 60 perch. then he dropped the nets
protecting the pens, allowing bass to swarm in, and counted the number of perch killed after two hours.
A regression analysis was performed on the 16 data points using x = number of perch in pen and y =
proportion of perch killed. Here is a residual plot and a histogram of the residuals.
0,4 -
0.3
0.2
0.1-
0.0
-0.1 -
-0.2-
-0.3 -
-0.4
10
20
30
40
50
60
Number of perch
Starnes & Tabor, The Practice of Statistics, 6e, © 2018
Bedford, Freeman & Worth High School Publishers
3
-0.4 -0.3 -0.2 -0.1
0.0
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Residual
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Transcribed Image Text:Here is one way in which nature regulates the size of animal populations: high population dehslty attracts predators, which remove a higher proportion of the population than when the density of the prey is low. One study looked at kelp perch and their common predator, the kelp bass. On each of four occasions, the researcher set up four large circular pens on sandy ocean bottoms off the coast of southern California. He randomly assigned young perch to 1 of 4 pens so that one pen had 10 perch, one pen had 20 perch, one pen had 40 perch and the final pen had 60 perch. then he dropped the nets protecting the pens, allowing bass to swarm in, and counted the number of perch killed after two hours. A regression analysis was performed on the 16 data points using x = number of perch in pen and y = proportion of perch killed. Here is a residual plot and a histogram of the residuals. 0,4 - 0.3 0.2 0.1- 0.0 -0.1 - -0.2- -0.3 - -0.4 10 20 30 40 50 60 Number of perch Starnes & Tabor, The Practice of Statistics, 6e, © 2018 Bedford, Freeman & Worth High School Publishers 3 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 03 Residual MacBook Air D00 000 F4 FI F2 F3 FS F6 F7 トト F8 F9 F10 @ #3 2$ & * 3 6. 8 W E R Y U P 5 Frequency jenpisə
Predictor
Coef
Stdev.
t-ratio
0.12049
0.09269
1.30
0.215
Constant
Perch
0.008569
0.002456
3.49
0.004
S = 0.1886
R-Sq
46.5%
R-Sq(adj)
42.7%
!!
k whother the
et.
le
3. What is the value of SE,? Interpret this value
4. Find the critical value for a 90% confidence interval for the slope of the true regression line. Then
calculate and interpret the confidence interval
5. Based on the interval, is there convincing evidence of a linear association between number of perch
and percent killed? Explain
Transcribed Image Text:Predictor Coef Stdev. t-ratio 0.12049 0.09269 1.30 0.215 Constant Perch 0.008569 0.002456 3.49 0.004 S = 0.1886 R-Sq 46.5% R-Sq(adj) 42.7% !! k whother the et. le 3. What is the value of SE,? Interpret this value 4. Find the critical value for a 90% confidence interval for the slope of the true regression line. Then calculate and interpret the confidence interval 5. Based on the interval, is there convincing evidence of a linear association between number of perch and percent killed? Explain
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