If r xy = 0, then:
If the regression coefficients are both 0 then r is 0. The reasoning for either one of them being 0 holds true mathematically but in the econometrics sense, rxy = 0, means that there is no linear relationship between x and y as covariance is 0; so one of the regression coefficient being non-zero would indicate existence of a relationship between the two variables. Hence, option c is the most appropriate one.
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