Using a simple linear regression, obtain a statistical relationship between the
annual precipitation (independent variable) and runoff (dependent variable).
Plot the original precipitation and runoff data, showing the regression line,
regression equation and the R2 value. Plot the predicted runoff based upon the
precipitation using the linear model. Show the graph, the regression line, and R2
value.
Figure 1:
Precipitation
(mm)
934.5
973.3
807.3
944.6
869.7
1072.4
907.6
868.7
770.2
892.6
1015.2
Year
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
Runoff
(mm)
351.1
364
328.8
304.9
407.2
398.8
342.2
377.9
271.2
260.2
421.1
Figure 2:
1200
y = -1.3136x + 3524.4
1000
mm
800
Precipitation (mm)
R² = 0.0025
Runoff (mm)
600
y = -1.4273x + 3183.9
400
200
0
1980
Linear (Precipitation
(mm))
R² = 0.0079
1985
1990
Year
Linear (Precipitation
(mm))
1995
Comment on the relationship you have observed by examining the values of the
intercept, the slope and correlation coefficient. Discuss why the annual
precipitation/annual runoff relationship may not be well explained by this
regression model, as well as the physical basis for the observed intercept values.
The ten years, from the year 1982 until 1992, the amount of precipitation is on
average 920mm of precipitation; and the average amount of runoff is 360mm. The
decline of precipitation, if this is a typical linear digression, may indicate that the world is
getting warmer. While the amount of precipitation digresses at -1.3136x, the amount of
runoff digresses even more at -1.4273x. This is indicative that as precipitation
decreases in this small watershed, so too does runoff. Therefore the opposite would be
true, that the increase in precipitation in a watershed will lead to an increase in runoff.
The annual precipitation/annual runoff relationship may not be well explained by this
regression model because the amount of precipitation will most often not fall exactly on
the regression line. Some years will get more precipitation than expected and other
years will be less than expected; also the amount of runoff may change, comparative to
the amount of precipitation in the area. Therefore, this line of regression does not reflect
an exact annual precipitation/annual runoff relationship; but indicates an educated
average for the annual precipitation/annual runoff relationship.