An article gave a scatter 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 data on rainfall and runoff volume (n = 15) given below. The equation of the least squares line is y=-1.082 +0.82861x, r2 = 0.972, and s=5.63. 5 12 14 17 23 30 40 47 55 67 72 81 96 112 127 (a) Use the fact that s = 1.54 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 t 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. O Yes, precise information is available because the resulting interval is very narrow. O 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. decimal places.)

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An article gave a scatter 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 data on rainfall and runoff volume (n=15) given below. The
equation of the least squares line is y=-1.082 +0.82861x, r² = 0.972, and s = 5.63.
12 14 17 23 30 40 47 55 67 72 81 96 112 127
y 5 10 14 14 15 26 26 46 37 47 52 70 83 100 100
(a) Use the fact that s = 1.54 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.)
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.
O Yes, precise information is available because the resulting interval is very narrow.
O 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.
Transcribed Image Text:An article gave a scatter 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 data on rainfall and runoff volume (n=15) given below. The equation of the least squares line is y=-1.082 +0.82861x, r² = 0.972, and s = 5.63. 12 14 17 23 30 40 47 55 67 72 81 96 112 127 y 5 10 14 14 15 26 26 46 37 47 52 70 83 100 100 (a) Use the fact that s = 1.54 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.) 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. O Yes, precise information is available because the resulting interval is very narrow. O 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.
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