STATISTICAL TECHNIQUES AND TOOLS
CORRELATION COEFFICIENT COEFFICIENT OF DETERMINATION
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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Average values of y changes by 0.5 when x is increased by 1.
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Average values of x changes by 0.5 when y is increased by 1.
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x explains 25% of the variation in y.
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y explains 25% of the variation in x.
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Detailed explanation-1: -The value of the correlation coefficient is given to be 0.5. This means 25% of the variation in y-variable (dependent variable) is explained by the x-variable (independent variable). Hence, the correct answer is option(a) The x-variable explains 25% of the variability in the y-variable.
Detailed explanation-2: -Therefore among the four coefficient values presented, the strongest is-. 75 and the weakest are +. 25 and-. 25.
Detailed explanation-3: -As a rule of thumb, a correlation coefficient between 0.25 and 0.5 is considered to be a “weak” correlation between two variables. 2. This rule of thumb can vary from field to field. For example, a much lower correlation could be considered weak in a medical field compared to a technology field.