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: -A correlation coefficient of-0.8 indicates an exceptionally strong negative correlation, meaning that the two variables tend to move in opposite directions.
Detailed explanation-3: -Coefficient of determination, r2, is a measure of how much of the variability in one variable can be “explained by” variation in the other. For example, if r=0.8 is the correlation between two variables, then r2=0.64. Hence, 64% of the variability in one can be explained by differences in the other.