Consider the following data on x = rainfall volume (m 3 ) and y = runoff volume

Question

Consider the following data on x = rainfall volume (m3) and y = runoff volume (m3) for a particular location.

Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff.

State the appropriate null and alternative hypotheses.

H0: 1 = 0

Ha: 1 > 0

H0: 1 = 0

Ha: 1 < 0    

H0: 1 0

Ha: 1 = 0

H0: 1 = 0 [Correct]

Ha: 1 0 [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.)

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.)

(_______,______) m^3

x 6 12 14 19 23 30 40 49 55 67 72 79 96 112 127 y 4 10 13 15 15 25 27 46 38 46 53 70 82 99 103

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = -2.0968634 + 0.84575899 x
Sample size: 15
R (correlation coefficient) = 0.98904334
R-sq = 0.97820673
Estimate of error standard deviation: 4.9788447

Parameter estimates:

Analysis of variance table for regression model:

Hence,

t = 24.16

P - value = 0.000

95% confidence interval: (0.770, 0.921)

Parameter Estimate Std. Err. DF 95% L. Limit 95% U. Limit Intercept -2.0968634 2.2689673 13 -6.9986692 2.8049423 Slope 0.84575899 0.035012314 13 0.77011948 0.9213985

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