Given the following sample observations, draw a scatter diagram on a separate pi
ID: 3154869 • Letter: G
Question
Given the following sample observations, draw a scatter diagram on a separate piece of paper. (Round your answers to 3 decimal places.)
X:
-8
-15
13
4
16
Y:
56
246
157
2
340
The coefficient of correlation is .
Does the relationship between the variables appear to be linear?
Given the following sample observations, draw a scatter diagram on a separate piece of paper. (Round your answers to 3 decimal places.)
X:
-8
-15
13
4
16
Y:
56
246
157
2
340
The coefficient of correlation is .
Does the relationship between the variables appear to be linear?
Try squaring the X- variable and then determine the correlation coefficient. .
Explanation / Answer
a.
Correlation
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 /5 (3351) - [ 1/5 *10 ] [ 1/5 *801] = 349.8
S. D ( X ) = Sqrt( 1/5*730-(1/5*10)^2) 11.916
S .D (Y) = Sqrt( 1/5*203905-(1/5*801)^2) 122.951
r(x,y) = 349.8 / 11.916*122.951 = 0.2388
If r = 0.2388> 0 ,Positive Correlation
b. SQUARE THE X VARIABLE
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 /5 (172539) - [ 1/5 *730 ] [ 1/5 *801] = 11118.6
S. D ( X ) = Sqrt( 1/5*149074-(1/5*730)^2) 92.189
S .D (Y) = Sqrt( 1/5*203905-(1/5*801)^2) 122.951
r(x,y) = 11118.6 / 92.189*122.951 = 0.9809
If r = 0.9809> 0 ,Perfect Positive Correlation
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