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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all the points on the scatterplot must fall exactly on a straight line with a positive slope.
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all the points on the scatterplot must fall exactly on a straight line with a negative slope.
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all the points on the scatterplot must fall exactly on a straight horizontal line.
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all the points on the scatterplot must fall exactly on a straight vertical line.
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Detailed explanation-1: -Answer and Explanation: If the correlation coefficient is exactly r=1, then c. all the data points must fall exactly on a straight line with a positive slope.
Detailed explanation-2: -A correlation coefficient of zero indicates that no linear relationship exists between two continuous variables, and a correlation coefficient of −1 or +1 indicates a perfect linear relationship. The strength of relationship can be anywhere between −1 and +1.
Detailed explanation-3: -Finally, if the points on a scatter plot line up in a perfectly straight line with a positive slope, we have a correlation coefficient of equals one.
Detailed explanation-4: -The correlation coefficient always takes a value between-1 and 1, with 1 or-1 indicating perfect correlation (all points would lie along a straight line in this case).