Stream gauge. Stream gauging is the process of measuring the water discharge or f low at a particular point in a stream or a river. Farmer W.H. (2019) demonstrated how multiple linear regression is applied on 293 stream gauges in the conterminous United States. (https://www.sciencebase.

gov/catalog/item/5ba90b60e4b08583a5ca04a3). By using the data in the research, five explanatory variables are selected to predict the 90th percentile of the annual maximum daily streamf low (max90) time series for the given stream gauge, and the following regression model was determined:

max 90 = -9836.23 + 2.02 DRAIN_SQKM

+ 70.24 PPTAVG_BASIN

+ 36.72 T_AVG_BASIN

+ 429.64 T_AVG_SITE

+ 54.8 RH_BASIN where DRAIN_SQKM is the drainage area of the stream gauge, PPTAVG_BASIN is the average precipitation over the basin, T_AVG_BASIN is the average temperature over the basin, T_AVG_SITE is the average temperature at the location of the stream gauge, and RH_BASIN is the average relative humidity over the basin.

Only the t-statistics of DRAIN_SQKM and PPTAVG_ BASIN coefficients have P-values < 0.001.

a) The analysis claims that with bigger drainage area of the stream gage will produce higher 90th percentile of the annual maximum daily streamflow. Does the coefficient of the DRAIN_SQKM demonstrate that? Explain.

b) The F-statistic for this model is 23.1264 (5, 287 df).

What do you conclude about the model?

c) If DRAIN_SQKM is removed as a predictor, then the F-statistic drops to 10.1259 and only PPTAVG_BASIN remains to be significant with a P-value < 0.05. Reconsider your interpretation in part a.