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Edit Vievw Bookmarks PeopleWindow Help 017 Secure https:/www.mathol.com(st ldn 44243 Mth 139 Fall Semester 2017 Sections 013,019 mchammad salameh&12/1017 5:48 PM Homework: Sec 9.3 -Score: 0.5 of 1 pt 9.3.33-T Hw Score: 83.33%, 2.5 of 3 pts Question Hep * The money raised and spent (both in mlions of dollars) by all congressional campasigns for 8 recent 2-year periods are shown in the table. The equation of the ine is y 0933 37 052 Find the coefficient of determination and intarpnet the resut alley 4699 1224.415 650 9 791 4 43 9 1026 9 1002.9 966 9 948 5 792.1 Find the coefficient of detemination and interpnet the resut 2.0 Round to three decimal places as needed) Success Enter your answer in the answer box and then click Check Answer B98 2 3 7 0

Explanation / Answer

9.3.33.

a.

calculation procedure for regression

mean of X = X / n = 830.9625

mean of Y = Y / n = 812.4875

(Xi - Mean)^2 = 382264.598

(Yi - Mean)^2 = 337603.65

(Xi-Mean)*(Yi-Mean) = 356720.906

b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2

= 356720.906 / 382264.598

= 0.933

bo = Y / n - b1 * X / n

bo = 812.4875 - 0.933*830.9625 = 37.052

value of regression equation is, Y = bo + b1 X

Y'=37.052+0.933* X

b.

calculation procedure for correlation

sum of (x) = x = 6647.7

sum of (y) = y = 6499.9

sum of (x^2)= x^2 = 5906254.01

sum of (y^2)= y^2 = 5618691.15

sum of (x*y)= x*y = 5757894.06

to caluclate value of r( x,y) = covariance ( x,y ) / sd (x) * sd (y)

covariance ( x,y ) = [ x*y - N *(x/N) * (y/N) ]/n-1

= 5757894.06 - [ 8 * (6647.7/8) * (6499.9/8) ]/8- 1

= 44590.113

and now to calculate r( x,y) = 44590.113/ (SQRT(1/8*5757894.06-(1/8*6647.7)^2) ) * ( SQRT(1/8*5757894.06-(1/8*6499.9)^2)

=44590.113 / (218.593*205.427)

=0.993

value of correlation is =0.993

coeffcient of determination = r^2 = 0.986

properties of correlation

1. If r = 1 Corrlation is called Perfect Positive Corrlelation

2. If r = -1 Correlation is called Perfect Negative Correlation

3. If r = 0 Correlation is called Zero Correlation

& with above we conclude that correlation ( r ) is = 0.993> 0 ,perfect positive correlation

Line of Regression Y on X i.e Y = bo + b1 X X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 469.9 446.5 130366.129 133946.85 132144.362 659.9 681.4 29262.379 17183.933 22424.155 727.2 749.7 10766.656 3942.27 6514.988 792.1 766.7 1510.294 2096.495 1779.417 791.4 743.9 1565.191 4704.245 2713.493 1026.9 1002.9 38391.504 36256.92 37308.949 955.9 948.5 15609.379 18499.4 16993.062 1224.4 1160.3 154793.066 120973.535 136842.48

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