3. Herbicide bioassay is concerned with the reduction in plant growth as a function of the...

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3. Herbicide bioassay is concerned with the reduction in plant growth as a function of the herbicide dose applied. This is of interest when developing new herbicides, assessing environmental effects on non-target species or estimating the residual herbicides in a treated soil before planting a new, herbicide susceptible, crop. A typical experiment would comprise a series of doses ranging from ineffective to severely damaging to establish a dose-response relationship. In this experiment, the callus area of a tissue culture of Brassica napus was measured corresponding to different doses of a sulfonylurea herbicide, chlorsulfuron. Consider the data below: Yi I y 0.25 7.35 where r represents the concentration of chlorsulfuron to the 0.3 power, and y represents the log of the callus area. Consider the dose-response model: 0.45 7.20 0.70 6.60 1.00 3.40 1.40 1.50 2.00 0.80 Report your estimate of SSE(0) for your "best" a 1+exp(01 (T₁-0₂)) where, in this experiment, a is known to be a = 7.6, and thus, is fixed. (NOTE: You should use R to do the calculations in this problem but, don't use a package or function to get the solutions!) a) Estimate the parameters 01, 02 by a grid search using the candidate values: 0₁ = {2.5, 2.75, 3, 3.25, 3.5, 3.75, 4, 4.25, 4.5,1.75} +€. I 0₂1-6, 7, 8, 9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5} parameter estimates. 3. Herbicide bioassay is concerned with the reduction in plant growth as a function of the herbicide dose applied. This is of interest when developing new herbicides, assessing environmental effects on non-target species or estimating the residual herbicides in a treated soil before planting a new, herbicide susceptible, crop. A typical experiment would comprise a series of doses ranging from ineffective to severely damaging to establish a dose-response relationship. In this experiment, the callus area of a tissue culture of Brassica napus was measured corresponding to different doses of a sulfonylurea herbicide, chlorsulfuron. Consider the data below: Yi I y 0.25 7.35 where r represents the concentration of chlorsulfuron to the 0.3 power, and y represents the log of the callus area. Consider the dose-response model: 0.45 7.20 0.70 6.60 1.00 3.40 1.40 1.50 2.00 0.80 Report your estimate of SSE(0) for your "best" a 1+exp(01 (T₁-0₂)) where, in this experiment, a is known to be a = 7.6, and thus, is fixed. (NOTE: You should use R to do the calculations in this problem but, don't use a package or function to get the solutions!) a) Estimate the parameters 01, 02 by a grid search using the candidate values: 0₁ = {2.5, 2.75, 3, 3.25, 3.5, 3.75, 4, 4.25, 4.5,1.75} +€. I 0₂1-6, 7, 8, 9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5} parameter estimates.

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