Question

An agricultural research station is trying to determine the relationship between the yield of sunflower seeds and the amount of fertilizer applied and the quality of soil (on the 10-point scale). To determine the relationship, five different fields were planted. In each field, four different plots were defined. In each plot, a different amount of fertilizer was used. The plot assignments for the fertilizer application were randomly selected in each field.

Pounds of Sunflower Seeds (per Acre)	Quality of soil	Pounds of Fertilizer (per Acre)
420	2.5	200
455	5	200
405	7.5	200
415	9	200
580	2.5	400
540	5	400
550	7.5	400
500	9	400
580	2.5	600
600	5	600
610	7.5	600
650	9	600
630	2.5	800
620	5	800
626	7.5	800
670	9	800
805	2.5	1000
830	5	1000
790	7.5	1000
775	9	1000

For all questions below, please use the actual names of the Dependent Variable and the Independent Variable

1. Based on the output tables, write down the regression equation.

2. What is the value of the estimated intercept? Interpret the value in terms of the amount of fertilizer, quality of soil and yield of sunflower seeds.

3. What are the values of the estimated slope for the variable “Quality of soil”?

4. What are the values of the estimated slope for the variable “Pounds of fertilizer”?

Answer 1

(1) Pounds of Sunflower Seeds (per Acre) = 353.3020 - 0.7837 * Quality of soil + 0.4233 * Pounds of Fertilizer (per Acre)

(2) Intercept = 353.3020. This is the Pounds of Sunflower Seeds (per Acre) when the soil quality was bad and no fertilizer was used. But the soil quality is measured on a 1-10 scale, so the intercept may not be much meaningful here.

(3) Slope = -0.7837

(4) Slope = 0.4233

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