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In a simple linear regression analysis, the following sum of squares are produced: ∑(y−y¯)2=500 ∑(y−y′)2=100 ∑(y′−y¯)2=400...

In a simple linear regression analysis, the following sum of squares are produced:

∑(y−y¯)2=500

∑(y−y′)2=100

∑(y′−y¯)2=400

The proportion of the variation in Y that is explained by the variation in X is:

a.) 80%

b.) 20%

c.) 50%

d.) 25%

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Answer #1

Solution :

From given data,

The proportion of the variation in Y that is explained by the variation in X is:

= 1 - (400 / 500)

= 1 - 0.80

= 0.20

= 20%

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