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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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

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 72 79 96 112 127
y 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
Predictor
Coef
Stdev
t-ratio
Constant
-1.431
2.601
-0.55
0.591
rainfall
0.83747
0.04021
20.83
0.000
s - 5.741
R-sg = 97.1%
R-sq (adj) - 96.9%
State the appropriate null and alternative hypotheses.
O Ho: P1 = 0
Hạ: B1 # 0
O Hoi Pq = 0
Hạ: B1 < 0
O Ho: Bị + 0
Hạ: ß1 = 0
O Họ: Pz = 0
Hạ: B1 > 0
Compute the test statistic value and find the P-value. (Round your test
statistic to two decimal places and your P-value to three decimal places.)
%3D
P-value =
State the conclusion in the problem context. (Use a = 0.05.)
O Reject Ho. There is a useful linear relationship between runoff and
rainfall at the 0.05 level.
O Reject Ho. There is not a useful linear relationship between runoff and
rainfall at the 0.05 level.
O Fail to reject Ho. There is not a useful linear relationship between runoff
and rainfall at the 0.05 level.
O 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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