DIRECTIONS: Show your work or explain how you arrived at your conclusion wheneve

Question

DIRECTIONS: Show your work or explain how you arrived at your conclusion whenever appropriate 1. In an area of the Great Plains, records were kept on the relationship between the annual rainfall (in inches) and the yield of wheat (bushels per acre). This data is in the table below 9.8 12. 18 9.6 6.3 Rainfall (inches) Yield of wheat (bushels/ acre) 47 18 65 72 50 0 42 56 60 Farmer Green used this data to predict the number of bushels per acre of wheat produced in a season based upon the number of inches of rainfall using linear regression analysis. His StatCrunch output is given below Farmer Green's output: Correlation between Rainfall (inches) and Yield (bushels) is: 0.86636001 (P-value 0.0025). Simple linear regression resultS: Dependent Variable: Yield (bushels) Independent Variable: Rainfall (inches) Yield (bushels) 8.5535 3.5724 Rainfall (inches) Fitted line Yield (bushels) 70 50 20 14 16 Rainfall (inches)

Explanation / Answer

SolutionA:

r=correlation coefficient=0.866

there exists a strong positive relationship between rainfall and yield of wheat

means as rainfall increases ,yield of wheat increases.and viceversa.

direction is positve

Solutonb:

since r=0.866 and p=0.005

p<0.05

Reject null hypothesis,Accept alternative hyotheesis and can conclude that there exists a relationship between rainall and yield.

regression equation is appropriate

Solutionc:

we have from regression eq is

yield=8.5535+3.5724*rainfall

for rainfall=15 inches

yield=8.5535+3.5724*15

yiled =62.1395

for 15 inches of rainfall predicted yield is 62.1 bushels

Solutiond:

yield=8.5535+3.5724*rainfall

for yiled=40

40=8.5535+3.5724*rainfall

rainfall=40-8.5535/3.5724

rainfall= 8.802626

rainfall=8.8

guess was reasonable as residual=8-8.8=-0.8

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