Just as you are about to estimate a regression (due tomorrow), massive sunspots
ID: 3125954 • Letter: J
Question
Just as you are about to estimate a regression (due tomorrow), massive sunspots cause magnetic interference that ruins all electrically powered machines (eg, computers). Instead of giving up and flunking, you decide to calculate estimates from your data (on per capita income in thousands of US dollars as a function of the percent of the labor force in agriculture in 10 developed countries).
Show your work.
i. Calculate B0 and B1.
ii. Calculate R squared and adjusted R squared.
iii. If the percent of the labor force in agriculture in another developed country was 8%, what level of per capita income (in thousands of dollars) would you guess the country had?
Explanation / Answer
i.Line of Regression Y on X i.e Y = bo + b1 X
Mean of X = X / n = 8.4
Mean of Y = Y / n = 7.1
(Xi - Mean)^2 = 26.4
(Yi - Mean)^2 = 40.9
(Xi-Mean)*(Yi-Mean) = -22.4
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
b1 = -22.4 / 26.4 = -0.8485
bo = Y / n - b1 * X / n
bo = 7.1 - -0.8485*8.4 = 14.2273
Y = bo + b1 X
Y'=14.2273-0.8485*X
ii.
r( X,Y) = Co V ( X,Y) / S.D (X) * S.D (y)
r( X,Y) = Sum(XY) / N- Mean of (X) * Mean of (Y) / Sqrt( X^2/n - ( Mean of X)^2 ) Sqrt( Y^2/n - ( Mean of Y)^2 )
Co v ( X, Y ) = 1 /10 (574) - [ 1/10 *84 ] [ 1/10 *71] = -2.24
S. D ( X ) = Sqrt( 1/10*732-(1/10*84)^2) 1.625
S .D (Y) = Sqrt( 1/10*545-(1/10*71)^2) 2.022
r(x,y) = -2.24 / 1.625*2.022 = -0.6817
If r = -0.6817< 0, Perfect Nagative Correlation
Coeffcient of determination = r^2 = 0.4647
iii.
When x = 8
Y'=14.2273-0.8485*X
=> Y = 14.2273-0.8485*(8) = 7.4393
X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 6 9 5.76 3.61 -4.56 8 10 0.16 8.41 -1.16 8 8 0.16 0.81 -0.36 7 7 1.96 0.01 0.14 7 10 1.96 8.41 -4.06 12 4 12.96 9.61 -11.16 9 5 0.36 4.41 -1.26 8 5 0.16 4.41 0.84 9 6 0.36 1.21 -0.66 10 7 2.56 0.01 -0.16Related Questions
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