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Which of the given options is NOT associated with the properties of the Principal Component?Select an option Clear ResponseThe Principal Components are orthogonal.The variation in the Principal Components increases from the 1st first Principal Component to the last one.The linear combinations of the original variables from the Principal ComponentsThe Principal Components helps in dimensionality reduction without information loss.

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Which of the given options is NOT associated with the properties of the Principal Component?Select an option Clear ResponseThe Principal Components are orthogonal.The variation in the Principal Components increases from the 1st first Principal Component to the last one.The linear combinations of the original variables from the Principal ComponentsThe Principal Components helps in dimensionality reduction without information loss.

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Solution

The statement "The variation in the Principal Components increases from the 1st first Principal Component to the last one" is NOT associated with the properties of the Principal Component.

In Principal Component Analysis (PCA), the first principal component accounts for the largest possible variance in the data set. Each succeeding component accounts for the highest possible remaining variance, under the constraint that it is orthogonal to (i.e., uncorrelated with) the preceding components. So, the variance (or the amount of information) actually decreases from the first to the last component, not increases.

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