Question

Consider the following data on x = rainfall volume (m3) and y = runoff volume (m3) for a particular location. x 5 12 14 16 23 30 40 47 55 67 72 83 96 112 127 y 4 10 13 14 15 25 27 45 38 46 53 67 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 = -1.82 + 0.839 rainfall Predictor Coef Stdev t-ratio p Constant -1.822 2.190 -0.83 0.420 rainfall 0.83897 0.03371 24.89 0.000 s = 4.859 R-sq = 97.9% R-sq(adj) = 97.8% State the appropriate null and alternative hypotheses. 1 H0: β1 = 0 Ha: β1 > 0 H0: β1 = 0 Ha: β1 < 0 H0: β1 ≠ 0 Ha: β1 = 0 H0: β1 = 0 Ha: β1 ≠ 0 Correct: Your answer is correct. 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 = 2 Correct: Your answer is correct. P-value = 3 Correct: Your answer is correct. State the conclusion in the problem context. (Use α = 0.05.) 4 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. Correct: Your answer is correct. 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.) 5 Incorrect: Your answer is incorrect. , 6 Incorrect: Your answer is incorrect. m3

I just need help with part D confidence interval

Answer 1

Coefficients:

Estimate Std. Error t value Pr(>|t|)   

(Intercept) -1.82244 2.19041 -0.832 0.42   

0.83897 0.03371 24.888 2.37e-12 **

Multiple R-squared: 0.9794, Adjusted R-squared: 0.9779

Confidence interval:

2.5 % 97.5 %

(Intercept) -6.5545239 2.9096506

0.7661451 0.9117937

Thus the 95% confidence interval for the true average change in runoff volume associated with a 1 m3 increase in rainfall volume ( ) is (0.766, 0.912)

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