This is the report which was submitted to the Soil and Water Conservation District by the Math 3620 students. The data set was provided to the University of Minnesota, Morris Mathematics 3690 - Topics in Statistics course. Some definitions are in order.

 JDAY : Julian day for the various years (93, 94, 95)

 CFS1 : Discharge rate in cubic feet per second - Pomme de Terre Morris Site

 CFS2 : Discharge rate in cubic feet per second - Pomme de Terre & Cty Rd 8 Site

 PRECIP : Precipitation sum of the previous five days

 To begin, examination of the basic relations which exist between the two sites is necessary.

 Note : Matrix deleted.

 This chart gives the correlation matrix for 1994. Here, we see that the discharge rates between the two sites are related 98% of the time. The correlation between the CFS and the Julian day indicate that the discharge rates decrease throughout the year at both sites.

 Note : Matrix and model deleted.

 Here, a regression model was created and tested to examine whether the discharge rate at site 2 could be predicted with knowledge of the site 1 discharge rate in 1994. An extremely low p-value (indicating the reliability of the model) acknowledges a strong model with the following characteristics :

 1994 : CFS2 = CFS1*(1.79)

 This model indicates that for every cubic foot per second increase at site 1, a 1.78 cubic foot per second increase would result at site 2. This is only one year, however, and we must further examine 1995 data.

 Note : Matrix deleted.

 This correlation matrix for 1995 indicate much the same information as 1994, yet the relation between site 1 and 2 is not as reliable, yet still quite significant. We will now examine the regression model.

 Note : Matrix and model deleted.

 This regression model is reliable, with an extremely low p-value. Therefore the following model can be built :

 1995 : CFS2 = CFS1 * 1.86

 This model indicates that for every cubic foot per second increase at site 1, a 1.86 cubic foot per second increase would result at site 2 in 1995. Now, knowing that it was only a 1.78 cu ft/sec increase in 1994, we can say that the impact of Muddy Creek on the Pomme de Terre River discharge rates increased. Now, we will examine whether the time of year makes a difference in these rates.

 Note : Matrix and model deleted.

 Here, in 1994, we examine the discharge rate at site 2, using the discharge rate at site 1 and the Julian day as indicators. Overall, the model is significant, and leads us to the following :

 1994 : CFS2 = CFS1*(2.02) - JDAY*(.299)

 The negative value associated with the Julian day indicates that the discharge rate decreases by approximately .3 cu ft/sec per day, and increases by 2.02 cu ft/sec for every cu ft/sec increase at site 1. With the additional variable of Julian day, the coefficient for CFS1 increased from 1.79 to 2.02. We will now repeat the analysis for 1995 and examine the coefficients.

 Note : Matrix and model deleted.

 This model is also highly reliable with the following :

 1995 : CFS2 = CFS1*(1.98) - JDAY*(.309)

 These appear to be highly efficient models for prediction. We see with the 1995 model, that the CFS1 coefficient decreases slightly from 2.02 to 1.98, fairly insignificant. Also, the JDAY coefficient rose from .299 to .309 from 1994 to 1995, also insignificant. Therefore, we will combine the data from 1994 and 1995 and create a general model.

 Note : Matrix and model deleted.

 This model best describes the interaction between the Pomme de Terre River, and the impact of Muddy Creek on discharge rates, depending on the time of year. The overall model is as follows :

 CFS2 = CFS1*(1.98) - JDAY*(.296)

 Interpretation is as follows. For every day that passes throughout the year, the discharge rate at site 2 decreases on average by .296 cu ft/sec. Then, for every cu ft/sec increase at site 1, the site 2 discharge rate increases by 1.98 cu ft/sec (nearly twice as much). Data collection through the following years will prove to add invaluable information to the data set.

 We will now turn to other graphical analysis regarding the time of year.

 Note : Figures deleted.

 This figure examine the discharge rates at site 1 over time. In 1994, the rates remained high until the Julian day was between 143 and 168 (May 23 to June 17). This range is wide, as these were the days of record taking. In 1995, the rates leveled off later in the year, between Julian day 146 and 180 (May 26 and June 29). We will now turn to examination of the precipitation levels found in the area, and the impact on the discharge rates at site 1.

 Note : Figures deleted.

 These two figures examine the discharge rates vs. precipitation from 1994. The figure on the left includes all data points, while the one on the right includes only the data points after the "leveling off" point, those after Julian day 143 (May 23). There is little organization to the graph on the left, while the one on the right may be helpful in examining the discharge rates throughout the Summer.

 Note : Matrix and model deleted.

 This model predicts the CFS at site 1 in 1994, dependent upon the precipitation after Julian day 143 (May 23). The model is significant and leads to the following equation :

 1994 : CFS1 = PRECIP*(70.41)

 This indicates that with every inch of rainfall we received in 1994, the discharge rate increased by approximately 70 cu ft/sec. We will now examine the graphs and model for 1995, using only data with Julian days after 146 (May 26).

 Note : Matrix and model deleted.

 This model is not entirely reliable, with a p-value of 0.19. This is due mainly to the lack of data. In 1995, there were only 8 data points to create this model with. However, we can examine the coefficients in the mock model :

 1995 : CFS1 = PRECIP*(64.4)

 The coefficient for precipitation, indicating that with every inch of precipitation the discharge rate for site 1 will increase by 64.4 cu ft/sec, is lower than the 70.4 cu ft/sec for 1994. This can be easily explained by the lack of data. Overall, these can be used to predict the impact of precipitation on the discharge rates at site 1.

1994

1995

OVERALL