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 (See file Q5).

A. Based on the output tables, write down the regression equation (using the actual names of the DV and the IV):

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

C. What is the values of the estimated slope for the variable “Quality of soil”? Interpret the value in terms of actual names of IVs and the DV.

D. What is the values of the estimated slope for the variable “Pounds of fertilizer”? Interpret the value in terms of actual names of IVs and the DV.

E. Does Quality of soil significantly influence the Yield of Sunflower at the alpha level of 0.05? Make sure to show which values you use to make the decision.

F. Does Pounds of fertilizer significantly influence the Yield of Sunflower at the alpha level of 0.05?  Make sure to show which values you use to make the decision.

G. If we keep the Amount of fertilizer unchanged, how will the Yield of sunflowers change if we decrease the Quality of soil by one unit?

H. If we keep the Quality of soil unchanged, how will the Yield of sunflowers change if we decrease the Amount of fertilizer by five units?

Data:

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

Answer 1

(A) Pounds_of_Sunflower_Seeds(per Acre)=353.302-7837*Quality_of_Soil + 0.4233* Pounds_of_Fertilizer(per Acre)

(B) intercept=353.202,

if there fertilizer=0 ( not used ) and quality of soil is zero , then sunflower seed yield will be 353.202

C. What is the values of the estimated slope for the variable “Quality of soil”? Interpret the value in terms of actual names of IVs and the DV.

the slope for quality of soil is -0.7837, this is change in seed yield if the unit change is done in quality of soil provided fertilizer used remain fixed.

D. What is the values of the estimated slope for the variable “Pounds of fertilizer”? Interpret the value in terms of actual names of IVs and the DV.

slope for pounds of fertilizer is 0.4233, this is change in seed yield if the unit change is done in fertilizer used provided quality of soil remains fixed.

E. Does Quality of soil significantly influence the Yield of Sunflower at the alpha level of 0.05? Make sure to show which values you use to make the decision.

no, it is not significantly influence as the p-value=0.8299 is more than alpha=0.05

F. Does Pounds of fertilizer significantly influence the Yield of Sunflower at the alpha level of 0.05?  Make sure to show which values you use to make the decision.

yes, it is significantly influence as the p-value=0.000 is less than alpha=0.05

G. If we keep the Amount of fertilizer unchanged, how will the Yield of sunflowers change if we decrease the Quality of soil by one unit?

increase in seed yield =0.7837

H. If we keep the Quality of soil unchanged, how will the Yield of sunflowers change if we decrease the Amount of fertilizer by five units?

increase in seed yield=5*0.4233=2.1165

following information has been generated using ms-excel

Regression Statistics
Multiple R	0.956194
R Square	0.914307
Adjusted R Square	0.904226
Standard Error	39.75722
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	2	286700.1	143350.1	90.69137	8.51E-10
Residual	17	26870.82	1580.636
Total	19	313571
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	353.302	29.98647	11.78205	1.33E-09	290.0361	416.568
Quality of soil	-0.78367	3.592096	-0.21817	0.829897	-8.36233	6.794987
Pounds of Fertilizer (per Acre)	0.42325	0.031431	13.46607	1.69E-10	0.356937	0.489563

Pounds_of_Sunflower_Seeds(per Acre)=353.302-7837*Quality_of_Soil - 0.4233* Pounds_of_Fertilizer(per Acre)