Researchers at the Erosion Control Center (Department of ABE, University of Illinois) are studying the relationship between the continuous variables crop yield level (variable yield, measured in kg/m²), tillage passes (variable till, 2, 3, or 4), and soil erosion (variable erosion, measured in g/ m²) during the month of June. The SAS code to read the data and the corresponding data are provided below.

data abe;

input erosion yield till @@;

datalines;

28.4 3.2 3 34.2 4.6 4 40.3 9.3 3 33.9 3.7 4 29.6 3.8 4 36.4 5.2 3 32.6 4.3 4 35.3 6.1 4

33.2 3.5 4 33.0 4.0 2 29.6 2.9 4 24.8 3.2 3 37.3 6.2 2 40.3 7.3 2 45.7 8.7 3 41.1 6.9 2

42.3 7.3 2 31.6 3.3 3 33.6 4.3 3 30.6 3.3 4 34.6 5.3 3 39.3 5.3 2 38.3 6.3 2 41.3 7.3 2

;

run;

1c. [15 points]

1. Provide the estimated value of the slope for the explanatory variable erosion, and
   • interpret or describe the meaning of the slope value (including units).
2. Describe null hypothesis for the erosion effect, and
   • indicate if you would reject this hypothesis at alpha < 0.05 and justify your answer.

1d. [15 points]

1. Provide the PROC MIXED ESTIMATE statement to predict the yield for erosion = 5.9 and till = 2.
2. Provide
   • the predicted yield value at erosion = 5.9 and till = 2, and
   • the corresponding standard error.

1e. [10 points]

1. Consider a multiple regression model to describe erosion that is different from the one in question 1a. Provide the complete PROC MIXED and MODEL statements to describe the response variable erosion, including in the model only an intercept and a linear and a quadratic trend on yield.
2. Provide the complete PROC MIXED and MODEL statements that describes the response variable erosion including in the model an intercept, the linear effect of till, the linear effect of yield, and the interaction between the linear effects of till and yield.