Question

True or False: If the correlation coefficient between response variable and the independent variable (or predictor) is close to zero, then the predictor makes almost no contribution in the variation of the response. Briefly justify your conclusion.

Answer 1

If correlation coefficient is close to zero it means that linear relationship between predictor and response variable doesn't exist. correlation coefficient tells about linear relationship only. But it is possible that independent variable related to response variable non-linearly.

Given statement is false.

And predictor variable may contribute in variation of response variable only if correlation is zero, because correlation coefficient is measure of only linear relationship.

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