5. Consider an experiment in which the mean yield of a certain crop is studied a

Question

5. Consider an experiment in which the mean yield of a certain crop is studied as a function of the amount of rain in inches) and the type of fertilizer (A or B) that was used during the growing season. The following models have been proposed to analyze the data: (i) Au(yield data Bo B1rain (ii) Au(yield data Bo in Brrain (iii) pu(yield data Bo B1rain +Brfertalizer, where fertilizer is a continuos vai able corresponding to the amount of fertilizer used (without distinguishing by type (iv) Au(yield data Bo rain BrfertA, where fertA is and indicator variable taking the value 1 when fertilizer A was used. (v) pu(yield data Po B1Tain Bofert A Barain x fertA, where fertA is and indicator variable taking the value 1 when fertilizer A was used.

Explanation / Answer

Part-a

Corresponding to 1 inch increase in rain there is on an average 1 change in yield, holding all else being equal.

Part-b

In model (ii) 2 means tells how effect of rain changes nonlinearly on yield.

In model-iii, the 2 tells the average change in yield corresponding to unit increase in amount of fertilizer.

Part-c

Model-ii is non linear as it has square term

Model-v is non linear as it has interaction term

Part-d

95% confidence interval means for all cases where rain is 10.1 inches and fertilizer is of type B, the average yield is 18.496 to 24.496 .

95% prediction interval means for all individual case where rain is 10.1 inches and fertilizer is of type B, the indivudal yield is 18.496 to 24.496 .

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