Consider the following data on x = rainfall volume (m³) and y = runoff volume (m³) for a particular location. x7 12 14 17 23 30 40 52 55 67 72 81 96 112 127 y 4 10 13 14 15 25 27 48 38 46 53 70 8299 102 Use the general software output to decide whether there is a useful linear relationship between rainfall and runoff. Predictor Intercept rainfall Coef Stdev -2.125 2.213 -0.96 0.842 0.034 t p-value 0.3546 24.77 0.0000 97.8% s 4.851 R-sq 97.9% R-sq (adj) State the least squares regression equation. ŷ: = State the appropriate null and alternative hypotheses. O Ho: B₁ = 0 Ho: B₁ = 0 O Ho: B₁ 0 Ha: B1 = 0 ○ Ho: B1 = 0 H: B₁ = 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.) P-value= State the conclusion in the problem context. (Use α = 0.05.) 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.)
Consider the following data on x = rainfall volume (m³) and y = runoff volume (m³) for a particular location. x7 12 14 17 23 30 40 52 55 67 72 81 96 112 127 y 4 10 13 14 15 25 27 48 38 46 53 70 8299 102 Use the general software output to decide whether there is a useful linear relationship between rainfall and runoff. Predictor Intercept rainfall Coef Stdev -2.125 2.213 -0.96 0.842 0.034 t p-value 0.3546 24.77 0.0000 97.8% s 4.851 R-sq 97.9% R-sq (adj) State the least squares regression equation. ŷ: = State the appropriate null and alternative hypotheses. O Ho: B₁ = 0 Ho: B₁ = 0 O Ho: B₁ 0 Ha: B1 = 0 ○ Ho: B1 = 0 H: B₁ = 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.) P-value= State the conclusion in the problem context. (Use α = 0.05.) 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.)
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:Consider the following data on x = rainfall volume (m³) and y = runoff volume (m³) for a particular location.
x 7 12 14 17 23 30 40 52 55 67 72 81 96 112 127
4 10 13 14 15 25 27 48 38 46 53 70 82 99 102
Use the general software output to decide whether there is a useful linear relationship between rainfall and runoff.
Predictor
Intercept
Coef
-2.125
Stdev
2.213
t
p-value
rainfall
0.842
0.034
-0.96
24.77
0.3546
0.0000
S
= 4.851 R-sq
=
97.9%
R-sq (adj)
=
97.8%
State the least squares regression equation. ŷ
=
State the appropriate null and alternative hypotheses.
0
Hoẞ1
H₂ B₁₁ < 0
○ Ho B₁ = 0
B1
H₂: B₁ => 0
1
O Ho: B₁ = 0
1
Ha B1 =
B1
= 0
○ Ho: B₁ = 0
Ha B₁ = 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.)
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.
3
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.)
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