1) Show that the sum of the deviations Σ(x-xbar) is always 0.
2) If x and y are collinear, i.e. y=a+bx, show that r^2=1
2) If x and y are collinear, i.e. y=a+bx, show that r^2=1
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I wish to answer ONLY one question at a time.
1) One of the mathematical properties of the Arithmetic Mean is that the sum of the deviations of items taken from their mean is always = 0
Let the data set is
X : 23 32 40 60 55
Arithmetic Mean = xbar = sigma X / N = 210/5 = 42
sigma (x - xbar) = (23-42)+(32-42)+(40-42)+(60-42)+(55-42)
= - 19 - 10 - 2 +18 + 13
= 0
Hence proved.
1) One of the mathematical properties of the Arithmetic Mean is that the sum of the deviations of items taken from their mean is always = 0
Let the data set is
X : 23 32 40 60 55
Arithmetic Mean = xbar = sigma X / N = 210/5 = 42
sigma (x - xbar) = (23-42)+(32-42)+(40-42)+(60-42)+(55-42)
= - 19 - 10 - 2 +18 + 13
= 0
Hence proved.