The article Approach to Confidence Interval Estimation for C

The article \"Approach to Confidence Interval Estimation for Curve Numbers\", discusses the relationship between rainfall depth and runoff depth at several locations. At one particular location, rainfall depth and runoff depth were recorded for 13 rainstorms. The following presents the MINITAB output for a fit of the least-squares line to predict runoff depth from rainfall depth (both measured in inches):

(b) Jeremy claims that if two storms differ in their rainfall by 1.0 inches, then their runoffs will differ, on the average, by 1.0 inches as well. Is this a plausible claim? Explain.

(c) It is a fact that if the rainfall is 0, the runoff is 0. Is the least squares line consistent with this fact? Explain.

Solution

a) The regression equation is given by Run off = -0.23+0.73 *Rain fall

when rain fall is 2.5 inches then run off = -0.23 + 0.73*2.5 =1.595

b) No. because the regression coefficient (slope ) is 0.73. means if the difference in rain fall is 1.0 inch then the corresponding difference in Runoff is 0.73

c) Since the p-value for the regression coefficient is 0.000 < 0.05(0.01) , the significance level, the least squares line is not consistent with the given fact