The reason why curvilinear relationships are hard to detect with correlation coefficients ( r) is because r always looks for the best straight line to fit the data. The correlation coefficient (r) is a measure of the closeness of association of the points in a scatter plot to a linear regression line based on those points for accumulated saving over time.
A curvilinear relationship is a type of relationship that exists between two variables that has a pattern of correspondence or association between the two variables that change as the values of the variables change.
Therefore, the correct answer is as given above
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