Consider the following data on x = rainfall volume (m³) and y = runoffvolume (m³) for a particular location.x 6 12 14 17 23 30 40 47 55 67 72 79 96 112 127y 4 10 13 14 15 25 27 46 38 46 53 74 82 99 100Use the accompanying Minitab output to decide whether there is a usefullinear relationship between rainfall and runoff.The regression equation isrunoff = -1.43 + 0.837 rainfallPredictorCoefStdevt-ratioConstant-1.4312.601-0.550.591rainfall0.837470.0402120.830.000s - 5.741R-sg = 97.1%R-sq (adj) - 96.9%State the appropriate null and alternative hypotheses.O Ho: P1 = 0Hạ: B1 # 0O Hoi Pq = 0Hạ: B1 < 0O Ho: Bị + 0Hạ: ß1 = 0O Họ: Pz = 0Hạ: B1 > 0Compute the test statistic value and find the P-value. (Round your teststatistic to two decimal places and your P-value to three decimal places.)%3DP-value =State the conclusion in the problem context. (Use a = 0.05.)O Reject Ho. There is a useful linear relationship between runoff andrainfall at the 0.05 level.O Reject Ho. There is not a useful linear relationship between runoff andrainfall at the 0.05 level.O Fail to reject Ho. There is not a useful linear relationship between runoffand rainfall at the 0.05 level.O Fail to reject Ho. There is a useful linear relationship between runoff andrainfall at the 0.05 level.Calculate a 95% confidence interval for the true average change in runoffvolume associated with a 1 m3 increase in rainfall volume. (Round youranswers to three decimal places.)m3

Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case you require the unanswered parts also, kindly re-post that parts separately. Given claim: Test whether there exists a linear relationship between rain fall and runoff. Null Hypothesis: H0:β1=0 Alternative Hypothesis: H0:β1≠0 Correct option: From the minitab output, t value corresponding with rainfall is 20.83 and the p value is 0.000 Therefore, t=20.83 p=0.000 Decision Rule: If p-value ≤ α, then reject the null hypothesis. Conclusion: The level of significance is α=0.05 Here, the p-value is less than the level of significance. From the decision rule, reject the null hypothesis. Correct option:

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Statistics

Consider the following data on x = rainfall volume (m³) and y = runoff volume (m3) for a particular location. x|6 12 14 17 23 30 40 47 55 67 2 79 96 112 127 | 4 10 13 14 15 25 27 46 38 46 53 74 82 99 100 Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff. The regression equation is runoff = -1.43 + 0.837 rainfall

Consider the following data on x = rainfall volume (m³) and y = runoff volume (m3) for a particular location. x|6 12 14 17 23 30 40 47 55 67 2 79 96 112 127 | 4 10 13 14 15 25 27 46 38 46 53 74 82 99 100 Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff. The regression equation is runoff = -1.43 + 0.837 rainfall

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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