plot, along with the least squares line, of x- rainfall volume (m³) and y runoff volume (m³) for a particular location. The simple linear regression model provides a very good fit to ta on rainfall and runoff volume (n-15) given below. The equation of the least squares line is y--2.364 + 0.84267x, -0.976, and s=5.21. x 5 12 14 17 23 30 40 47 55 67 72 81 96 112 127 y 3 9 12 14 14 24 27 45 38 46 52 71 81 100 101 (a) Use the fact that s = 1.43 when rainfall volume is 40 m³ to predict runoff in a way that conveys information about reliability and precision. (Calculate a 95% PI. Round your answers to two decimal places.) 28.25 1x ) m³ Does the resulting interval suggest that precise information about the value of runoff for this future observation is available? Explain your reasoning. O Yes, precise information is available because the resulting interval is very wide. x 34.46 O Yes, precise information is available because the resulting interval is very narrow. No, precise information is not available because the resulting interval is very wide. O No, precise information is not available because the resulting interval is very narrow. (b) Calculate a 95% PI for runoff when rainfall is 50. (Round your answers to two decimal places.) 36.8253 x 42.72 x )m³ What can be said about the simultaneous prediction level for the two intervals you have calculated? The simultaneous prediction level for the intervals is at least 28.54 X%.
plot, along with the least squares line, of x- rainfall volume (m³) and y runoff volume (m³) for a particular location. The simple linear regression model provides a very good fit to ta on rainfall and runoff volume (n-15) given below. The equation of the least squares line is y--2.364 + 0.84267x, -0.976, and s=5.21. x 5 12 14 17 23 30 40 47 55 67 72 81 96 112 127 y 3 9 12 14 14 24 27 45 38 46 52 71 81 100 101 (a) Use the fact that s = 1.43 when rainfall volume is 40 m³ to predict runoff in a way that conveys information about reliability and precision. (Calculate a 95% PI. Round your answers to two decimal places.) 28.25 1x ) m³ Does the resulting interval suggest that precise information about the value of runoff for this future observation is available? Explain your reasoning. O Yes, precise information is available because the resulting interval is very wide. x 34.46 O Yes, precise information is available because the resulting interval is very narrow. No, precise information is not available because the resulting interval is very wide. O No, precise information is not available because the resulting interval is very narrow. (b) Calculate a 95% PI for runoff when rainfall is 50. (Round your answers to two decimal places.) 36.8253 x 42.72 x )m³ What can be said about the simultaneous prediction level for the two intervals you have calculated? The simultaneous prediction level for the intervals is at least 28.54 X%.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:An article gave a scatter plot, along with the least squares line, of x = rainfall volume (m³) and y
data on rainfall and runoff volume (n
= runoff volume (m³) for a particular location. The simple linear regression model provides a very good fit to
15) given below. The equation of the least squares line is y = -2.364 + 0.84267x, ² 0.976, and s = 5.21.
=
x 5 12 14 17 23 30 40 47 55 67
72
81 96 112 127
y 3 9 12 14 14 24 27 45 38 46 52 71 81 100 101
(a) Use the fact that s = 1.43 when rainfall volume is 40 m³ to predict runoff in a way that conveys information about reliability and precision. (Calculate a 95% PI. Round your answers to two decimal
places.)
Ŷ
28.25
1x ) m³
Does the resulting interval suggest that precise information about the value of runoff for this future observation is available? Explain your reasoning.
OYes, precise information is available because the resulting interval is very wide.
34.46
Yes, precise information is available because the resulting interval is very narrow.
No, precise information is not available because the resulting interval is very wide.
O No, precise information is not available because the resulting interval is very narrow.
(b) Calculate a 95% PI for runoff when rainfall is 50. (Round your answers to two decimal places.)
36.8253
X 42.72
xm³
L
What can be said about the simultaneous prediction level for the two intervals you have calculated?
The simultaneous prediction level for the intervals is at least 28.54
X %.
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