Prediction of dissolved oxygen in rivers. A research article published in Hindawi, Complexity (2020) predicted the dissolved oxygen (DO) in the Nyando River basin in Kenya. To understand the influence of the factors contributing to DO variations, the models considered the inputs from the available water quality parameters (WQPs) including discharge, electrical conductivity (EC), pH, turbidity, temperature, total phosphates (TPs), total suspended solids (TSSs), and total nitrates (TNs). Two of the fitted models for DO 1y2 with their respective R2 values are given below: Model 1: E1y2 = b0 + b11EC2 + b21TP2 + b31TN2 + b41pH2 1R2 = 0.31182 Model 2: E1y2 = b0 + b11EC2 + b21TP2 + b31TN2 + b41pH2 + b51Turb2 + b61Discharge2 + b71Temp2 + b81TSS2 1R2 = 0.38442

a. Interpret the R2 -values for the models.

b. Give the null and alternative hypotheses for comparing the fits of models 1 and 2.

c. Are the two models nested? Explain

d. Say the nested F-test for comparing the two models resulted in F = 15.983 and p-value 6 .01. What can you conclude from these results?

e. A third model was fit, one that hypothesizes all possible pairs of interactions between discharge, turbidity, temperature and total suspended solids (TSSs). Give the equation of this model (model 3).

f. A nested F-test to compare models 2 and 3 resulted in a p@value 7 .10. What can you conclude from this result?