WHat is the confidence interval? Consider the following data on x = rainfall volume (m3) and y = runoff volume (m3) for a particular location. x 5 12 14 18 23 30 40 46 55 67 72 83 96 112 127 y 4 10 13 14 15 25 27 45 38 46 53 71 82 99 105 Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff. The regression equation is runoff = -2.05 + 0.847 rainfall Predictor Coef Stdev t-ratio p Constant -2.049 2.251 -0.91 0.379 rainfall 0.84717 0.03465 24.45 0.000 s = 4.978 R-sq = 97.9% R-sq(adj) = 97.7% State the appropriate null and alternative hypotheses. H0: β1 = 0 Ha: β1 ≠ 0 H0: β1 ≠ 0 Ha: β1 = 0 H0: β1 = 0 Ha: β1 < 0 H0: β1 = 0 Ha: β1 > 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.) t = P-value = State the conclusion in the problem context. (Use α = 0.05.) Reject H0. There is a useful linear relationship between runoff and rainfall at the 0.05 level.Reject H0. There is not a useful linear relationship between runoff and rainfall at the 0.05 level. Fail to reject H0. There is not a useful linear relationship between runoff and rainfall at the 0.05 level.Fail to reject H0. 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.)
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.
WHat is the confidence interval?
Consider the following data on x = rainfall volume (m3) and y = runoff volume (m3) for a particular location.
| x | 5 | 12 | 14 | 18 | 23 | 30 | 40 | 46 | 55 | 67 | 72 | 83 | 96 | 112 | 127 |
| y | 4 | 10 | 13 | 14 | 15 | 25 | 27 | 45 | 38 | 46 | 53 | 71 | 82 | 99 | 105 |
Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff.
| The regression equation is runoff = -2.05 + 0.847 rainfall |
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| Predictor | Coef | Stdev | t-ratio | p |
| Constant | -2.049 | 2.251 | -0.91 | 0.379 |
| rainfall | 0.84717 | 0.03465 | 24.45 | 0.000 |
| s = 4.978 R-sq = 97.9% R-sq(adj) = 97.7% |
State the appropriate null and alternative hypotheses.
Ha: β1 ≠ 0
Ha: β1 = 0
Ha: β1 < 0
Ha: β1 > 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.)
| t | = | |
| P-value | = |
State the conclusion in the problem context. (Use α = 0.05.)
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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