8.1 Assignment

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What is the correlation coefficient (r)?

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The correlation coefficient (r) is a statistical measure that describes the strength and direction of a relationship between two variables. It ranges from -1 to 1.

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What does a correlation coefficient of 1.00 indicate?

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A correlation coefficient of 1.00 indicates a perfect positive linear relationship between two variables.

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What does a correlation coefficient of -1.00 indicate?

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A correlation coefficient of -1.00 indicates a perfect negative linear relationship between two variables.

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What does a correlation coefficient of 0 indicate?

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A correlation coefficient of 0 indicates no linear relationship between the two variables.

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How do you interpret a correlation coefficient of 0.96?

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A correlation coefficient of 0.96 indicates a very strong positive linear relationship between the two variables.

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What is the formula for calculating the correlation coefficient (r)?

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The formula for calculating the correlation coefficient (r) is r = (nΣxy - ΣxΣy) / sqrt[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)], where n is the number of pairs, Σxy is the sum of the product of paired scores, Σx is the sum of x scores, and Σy is the sum of y scores.

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What is the significance of rounding the correlation coefficient to the nearest hundredth?

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Rounding the correlation coefficient to the nearest hundredth provides a more precise and standardized way to report the strength of the relationship.

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What are the limitations of using correlation coefficients?

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Correlation coefficients do not imply causation, can be affected by outliers, and only measure linear relationships.

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What is the difference between positive and negative correlation?

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Positive correlation means that as one variable increases, the other variable also increases. Negative correlation means that as one variable increases, the other variable decreases.

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What is a scatter plot and how is it related to correlation?

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A scatter plot is a graphical representation of two variables where each point represents an observation. It helps visualize the relationship and correlation between the variables.