Problem 3 The article \"Characterization of Highway Run of in Austin, Texas, Are

Question

Problem 3 The article "Characterization of Highway Run of in Austin, Texas, Area (I. of Envir. Engr., 1998: 131-137) gave data on rainfall volume (ms) and runoir vol Ile (n measured on 30 dillerent days for a particul location. We would like to determine how the runoff volume is affected b rainfall volume. Suuumary y statistics of data are: 53.2 sz 38-3. 42.9. 32.1 Ta 30. l. In view of the question we want to answer. what is the predictor variable, and what is the rosponse variable? 2. Suppose that the correlation coefficient between the rainfall volunc and the runoll volune is r 0.89. Find the least squares regression line equation 3. What is proportion of variation in the runofr volume explained by the rainfall volume? 4. For a day with the rainfall volume 72 m aud the runoff vol Lune 53 m what is the residual of this day for the predictiou using the above least square regression line?

Explanation / Answer

1. predictor variable = rainfall volume
response variable = runoff volume

2. r = 0.89
slope (b) = r (sy/sx) = 0.89*32.1/38.3 = 0.746
intercept (a) = `y - b`x = 42.9 - 0.746*53.2 = 3.2128
So, the regression line is runoff volume = 3.2128 + 0.746*rainfall volume

3. r^2 = 0.89^2 = 0.7921
So, 79.21% of variation in the runoff volume is explained by rainfall volume.

4. rainfall volume = 72
Predicted runoff volume = 3.2128 + 0.746*72 = 56.9248
Residual = Observed value - Predicted value = 53 - 56.9248 = -3.9248

5. When the rainfall volume increases by 1 m3, on average the runoff volume will increase by 0.746
When the rainfall volume is 0 m3, on average the runoff volume is 3.2128 m3

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