The article “Characterization of Highway Runoff in Austin, Texas, Area” (J. of E

Question

The article “Characterization of Highway Runoff in Austin, Texas, Area” (J. of Envir. Engr., 1998: 131-137) gave data on rainfall volume (m3 ) and runoff volume (m3 ) measured on 30 different days for a particular location. We would like to determine how the runoff volume is affected by rainfall volume. Summary statistics of data are: x = 53.2, sx = 38.3, y = 42.9, sy = 32.1, n = 30.

1. In view of the question we want to answer, what is the predictor variable, and what is the response variable?

2. Suppose that the correlation coefficient between the rainfall volume and the runoff volume is r = 0.89. Find the least squares regression line equation.

3. What is proportion of variation in the runoff volume explained by the rainfall volume?

4. For a day with the rainfall volume 72 m3 and the runoff volume 53 m3 , what is the residual of this day for the prediction using the above least square regression line?

Explanation / Answer

1. Response variable: Runoff volume, Predictor variable: Rainfall volume

2. Slope, b=r(Sy/Sx)=0.89(32.1/38.3)=0.75

Intercept, a=Ybar-bXbar=42.9-0.75*53.2=3

Runoff volume=3+0.75 rainfall volume

3. The coefficient of determination, R^2=0.7921. Therefore, 79.21% variation in runoff volume is expalined by the rainfall volume.

4. Runoff volume=3+0.75*72=57

Residual=obs-exp=53-57=-4

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.