18.2 James Jesse, the head of the Bureau of Animal Husbandry, perceives that sev
ID: 3227308 • Letter: 1
Question
18.2 James Jesse, the head of the Bureau of Animal Husbandry, perceives that several agencies received large increases in appropriations last year because they encouraged interest groups to testify for them before the House Appropriations Committee. The accompanying sample data for five agencies similar to Jesse’s were gathered. Using regression analysis, calculate a regression equation. Does a relationship exist? The Bureau of Animal Husbandry could pressure 15 groups to testify for it. What percentage increase in appropriation would this number of groups predict? Place a 90% confidence interval around that estimate. How large an increase is each additional interest group worth?
Interest Groups Testifying
Percentage Increase in Appropriation
25
22
14
17
7
8
18
19
Interest Groups Testifying
Percentage Increase in Appropriation
25
22
14
17
7
8
18
19
Explanation / Answer
x y x^2 y^2 xy
25 22 625 484 550
14 17 196 289 238
7 8 49 64 56
18 19 324 361 342
64 66 1194 1198 1186
b1= nE(xy)-ExEy/nE(x2)-(Ex2)
=4*1186-(64*66)/4*1194-(64*64)
=4744-4244/4776-4096
=500/680
=0.735294
b0=Ey-b1Ex/n
=66-0.735294*64/4
=35736-1863.48/25
=4.235294
Therefore, y=4.235294+0.735294x
r (correlation)=n(Exy)-(Ex)(Ey)/sqrt(nEx2-(Ex)2)(nEY2-(Ey)2)
=4*1186-(64*66)/sqrt*(4*1194)-(64*64)(4*1198-(66*66)
=4744-4244/sqrt*4776-4096*4792-4356
=500/544.50=0.918
r^2=0.918*0.918=0.843
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