Consider the following data on x = rainfall volume (m³) and y = runoff volume (m³) for a particular location. x 6 12 14 18 23 30 40 47 55 67 72 84 96 112 127 y 4 10 13 15 15 25 27 46 38 46 53 75 82 99 104 Use the general software output to decide whether there is a useful linear relationship between rainfall and runoff. Predictor Intercept rainfall Coef Stdev t p-value -1.986 2.367 -0.84 0.4165 0.849 0.036 23.36 0.0000 s = 5.216 R-sq = 97.7% R-sq(adj) = 97.5% State the least squares regression equation. ŷ: State the appropriate null and alternative hypotheses. O Ho: P₁-0 H₂ P<0 Ho: B₁ = 0 Ha B1 = 0 = O Ho: B1-0 H₂: B₁ = 0 ○ Ho: P₁ = 0 H₁₁> 0 From the output state the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) t= P-value= State the conclusion in the problem context. (Use α = 0.05.) O Reject Ho. There is a useful linear relationship between runoff and rainfall at the 0.05 level. Reject Ho. There is not a useful linear relationship between runoff and rainfall at the 0.05 level. Fail to reject Ho. There is not a useful linear relationship between runoff and rainfall at the 0.05 level. Fail to reject Ho. There is a useful linear relationship between runoff and rainfall at the 0.05 level. Calculate a 95% confidence interval for the true average change in runoff volume associated with a 1 m³ increase in rainfall volume. (Round your answers to three decimal places.) m³
Consider the following data on x = rainfall volume (m³) and y = runoff volume (m³) for a particular location. x 6 12 14 18 23 30 40 47 55 67 72 84 96 112 127 y 4 10 13 15 15 25 27 46 38 46 53 75 82 99 104 Use the general software output to decide whether there is a useful linear relationship between rainfall and runoff. Predictor Intercept rainfall Coef Stdev t p-value -1.986 2.367 -0.84 0.4165 0.849 0.036 23.36 0.0000 s = 5.216 R-sq = 97.7% R-sq(adj) = 97.5% State the least squares regression equation. ŷ: State the appropriate null and alternative hypotheses. O Ho: P₁-0 H₂ P<0 Ho: B₁ = 0 Ha B1 = 0 = O Ho: B1-0 H₂: B₁ = 0 ○ Ho: P₁ = 0 H₁₁> 0 From the output state the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) t= P-value= State the conclusion in the problem context. (Use α = 0.05.) O Reject Ho. There is a useful linear relationship between runoff and rainfall at the 0.05 level. Reject Ho. There is not a useful linear relationship between runoff and rainfall at the 0.05 level. Fail to reject Ho. There is not a useful linear relationship between runoff and rainfall at the 0.05 level. Fail to reject Ho. There is a useful linear relationship between runoff and rainfall at the 0.05 level. Calculate a 95% confidence interval for the true average change in runoff volume associated with a 1 m³ increase in rainfall volume. (Round your answers to three decimal places.) m³
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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![Consider the following data on x = rainfall volume (m³) and y = runoff volume (m³) for a particular location.
x 6 12 14 18 23 30 40 47 55 67 72 84 96 112 127
y 4 10 13 15 15 25 27 46 38 46 53 75 82 99 104
Use the general software output to decide whether there is a useful linear relationship between rainfall and runoff.
Predictor
Intercept
rainfall
Coef Stdev
t p-value
-1.986 2.367 -0.84 0.4165
0.849 0.036 23.36 0.0000
s = 5.216 R-sq = 97.7% R-sq(adj) = 97.5%
State the least squares regression equation. ŷ:
State the appropriate null and alternative hypotheses.
O Ho: P₁-0
H₂ P<0
Ho: B₁ = 0
Ha B1 = 0
=
O Ho: B1-0
H₂: B₁ = 0
○ Ho: P₁ = 0
H₁₁> 0
From the output state the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
t=
P-value=
State the conclusion in the problem context. (Use α = 0.05.)
O Reject Ho. There is a useful linear relationship between runoff and rainfall at the 0.05 level.
Reject Ho. There is not a useful linear relationship between runoff and rainfall at the 0.05 level.
Fail to reject Ho. There is not a useful linear relationship between runoff and rainfall at the 0.05 level.
Fail to reject Ho. There is a useful linear relationship between runoff and rainfall at the 0.05 level.
Calculate a 95% confidence interval for the true average change in runoff volume associated with a 1 m³ increase in rainfall volume. (Round your answers to three decimal places.)
m³](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb392b50f-f9c7-48cd-a379-2972074f7ee7%2F5f31b1d6-fd08-4c70-9d4f-fb6c4921899a%2Fn1znyhd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following data on x = rainfall volume (m³) and y = runoff volume (m³) for a particular location.
x 6 12 14 18 23 30 40 47 55 67 72 84 96 112 127
y 4 10 13 15 15 25 27 46 38 46 53 75 82 99 104
Use the general software output to decide whether there is a useful linear relationship between rainfall and runoff.
Predictor
Intercept
rainfall
Coef Stdev
t p-value
-1.986 2.367 -0.84 0.4165
0.849 0.036 23.36 0.0000
s = 5.216 R-sq = 97.7% R-sq(adj) = 97.5%
State the least squares regression equation. ŷ:
State the appropriate null and alternative hypotheses.
O Ho: P₁-0
H₂ P<0
Ho: B₁ = 0
Ha B1 = 0
=
O Ho: B1-0
H₂: B₁ = 0
○ Ho: P₁ = 0
H₁₁> 0
From the output state the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
t=
P-value=
State the conclusion in the problem context. (Use α = 0.05.)
O Reject Ho. There is a useful linear relationship between runoff and rainfall at the 0.05 level.
Reject Ho. There is not a useful linear relationship between runoff and rainfall at the 0.05 level.
Fail to reject Ho. There is not a useful linear relationship between runoff and rainfall at the 0.05 level.
Fail to reject Ho. There is a useful linear relationship between runoff and rainfall at the 0.05 level.
Calculate a 95% confidence interval for the true average change in runoff volume associated with a 1 m³ increase in rainfall volume. (Round your answers to three decimal places.)
m³
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