2452 Correlation Coefficients & Coefficients Of Determination

1)

For the data set above (Data 2), what is the value of Coefficient of Determination? (As a percentage to the nearest whole number)

Use bivardatasets to enter data, then page 1.6 to find your answer

Explanation

Use bivardatasets to enter data, then page 1.6 to find your answer

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2)

For the data set above (Data 3), what is the value of the Coefficient of Determination? (As a percentage to the nearest whole number)

The coefficient of determination measures the proportion of the variance in the dependent variable that can be explained by the independent variable(s). In this case, the value of the coefficient of determination is given as 85%. This means that 85% of the variance in the dependent variable can be explained by the independent variable(s) in the data set.

Explanation

The coefficient of determination measures the proportion of the variance in the dependent variable that can be explained by the independent variable(s). In this case, the value of the coefficient of determination is given as 85%. This means that 85% of the variance in the dependent variable can be explained by the independent variable(s) in the data set.

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4)

For the data set above (Data 4), what is the value of the

? (As a percentage to the nearest whole number)

The value of "?" in the given data set is 6%.

Explanation

The value of "?" in the given data set is 6%.

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5)

For the data set above (Data 4), what is the value of the Coefficient of Determination? (Answer as a percentage to the nearest whole number)

The value of the Coefficient of Determination for the given data set is 6%. The Coefficient of Determination, also known as R-squared, measures the proportion of the variance in the dependent variable that can be explained by the independent variable(s). In this case, 6% of the variance in the dependent variable can be explained by the independent variable(s) in the data set.

Explanation

The value of the Coefficient of Determination for the given data set is 6%. The Coefficient of Determination, also known as R-squared, measures the proportion of the variance in the dependent variable that can be explained by the independent variable(s). In this case, 6% of the variance in the dependent variable can be explained by the independent variable(s) in the data set.

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6)

For the data set above (Data 5 ), what is the value of the

? (As a percentage to the nearest whole number)

The value of "?" in the data set is 50%. This means that the unknown value represents half of the data set.

Explanation

The value of "?" in the data set is 50%. This means that the unknown value represents half of the data set.

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7)

For the data set above (Data 5 ), what is the value of the Coefficient of Determination? (Answer as a percentage to the nearest whole number)

The coefficient of determination, also known as R-squared, is a measure of how well the regression line fits the data points. It represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). In this case, the value of the coefficient of determination is given as 50%, which means that 50% of the variance in the dependent variable can be explained by the independent variable(s).

Explanation

The coefficient of determination, also known as R-squared, is a measure of how well the regression line fits the data points. It represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). In this case, the value of the coefficient of determination is given as 50%, which means that 50% of the variance in the dependent variable can be explained by the independent variable(s).

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9)

For the data set above (Data 6 ), what is the value of the Coefficient of Determination? (Answer as a percentage to the nearest whole number)

The coefficient of determination is a statistical measure that represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s). In this case, the value of the coefficient of determination is 64%. This means that 64% of the variance in the dependent variable can be explained by the independent variable(s) in the given data set.

Explanation

The coefficient of determination is a statistical measure that represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s). In this case, the value of the coefficient of determination is 64%. This means that 64% of the variance in the dependent variable can be explained by the independent variable(s) in the given data set.

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11)

For the data set above (Data 7 ), what is the value of the Coefficient of Determination? (Answer as a percentage to the nearest whole number)

The value of the Coefficient of Determination is 47%. The Coefficient of Determination, also known as R-squared, is a statistical measure that represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s). In this case, 47% of the variance in the dependent variable can be explained by the independent variable(s) in the given data set.

Explanation

The value of the Coefficient of Determination is 47%. The Coefficient of Determination, also known as R-squared, is a statistical measure that represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s). In this case, 47% of the variance in the dependent variable can be explained by the independent variable(s) in the given data set.

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13)

For the data set above (Data 8 ), what is the value of the Coefficient of Determination? (Answer as a percentage to the nearest whole number)

The coefficient of determination, also known as R-squared, measures the proportion of the variance in the dependent variable that can be explained by the independent variable(s). In this case, the value of the coefficient of determination is given as 52%. This means that 52% of the variance in the dependent variable can be explained by the independent variable(s) in the data set.

Explanation

The coefficient of determination, also known as R-squared, measures the proportion of the variance in the dependent variable that can be explained by the independent variable(s). In this case, the value of the coefficient of determination is given as 52%. This means that 52% of the variance in the dependent variable can be explained by the independent variable(s) in the data set.

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14)

For the data set above (Data 8 ), what is the value of the

? (As a percentage to the nearest whole number)

The value of "?" in the given data set is 18%.

Explanation

The value of "?" in the given data set is 18%.

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15)

For the data set above (Data 9 ), what is the value of the Coefficient of Determination? (Answer as a percentage to the nearest whole number)

The value of the Coefficient of Determination is 18%. This indicates that 18% of the variation in the dependent variable can be explained by the independent variable(s) in the data set.

Explanation

The value of the Coefficient of Determination is 18%. This indicates that 18% of the variation in the dependent variable can be explained by the independent variable(s) in the data set.

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16)

For the data set above (Data 10 ), what is the value of Coefficient of Determination? (Answer as a percentage to the nearest whole number)

The value of the Coefficient of Determination is 99%. This indicates that 99% of the variation in the dependent variable can be explained by the independent variable(s) in the data set.

Explanation

The value of the Coefficient of Determination is 99%. This indicates that 99% of the variation in the dependent variable can be explained by the independent variable(s) in the data set.

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17)

For the data set above, the Coefficient of Determination is 65.63%. What is the Correlation Coefficient? (2 decimal places)

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the coefficient of determination is given as 65.63%, which represents the proportion of the total variation in the dependent variable that can be explained by the independent variable. The correlation coefficient is the square root of the coefficient of determination, so the correlation coefficient in this case would be -0.81.

Explanation

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the coefficient of determination is given as 65.63%, which represents the proportion of the total variation in the dependent variable that can be explained by the independent variable. The correlation coefficient is the square root of the coefficient of determination, so the correlation coefficient in this case would be -0.81.

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18)

For the data set above, the Coefficient of Determination is 79.31%. What is the Correlation Coefficient? (2 decimal places)

The negative correlation coefficient of -0.89 indicates a strong negative linear relationship between the variables in the data set. This means that as one variable increases, the other variable tends to decrease. The coefficient of determination of 79.31% suggests that 79.31% of the variability in one variable can be explained by the variability in the other variable.

Explanation

The negative correlation coefficient of -0.89 indicates a strong negative linear relationship between the variables in the data set. This means that as one variable increases, the other variable tends to decrease. The coefficient of determination of 79.31% suggests that 79.31% of the variability in one variable can be explained by the variability in the other variable.

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19)

For the data set above, the Coefficient of Determination is 81.37%. What is the Correlation Coefficient? (2 decimal places)

The coefficient of determination is a measure of how well the regression line fits the data, representing the proportion of the variance in the dependent variable that can be explained by the independent variable. It is calculated by squaring the correlation coefficient. Therefore, to find the correlation coefficient, we need to take the square root of the coefficient of determination. In this case, the square root of 81.37% is 0.9137. However, since we need the correlation coefficient with two decimal places, it would be rounded to -0.90.

Explanation

The coefficient of determination is a measure of how well the regression line fits the data, representing the proportion of the variance in the dependent variable that can be explained by the independent variable. It is calculated by squaring the correlation coefficient. Therefore, to find the correlation coefficient, we need to take the square root of the coefficient of determination. In this case, the square root of 81.37% is 0.9137. However, since we need the correlation coefficient with two decimal places, it would be rounded to -0.90.

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20)

For the data set above, the Coefficient of Determination is 67.12%. What is the Correlation Coefficient? (2 decimal places)

The negative value of the correlation coefficient (-0.82) indicates a strong negative linear relationship between the variables in the data set. This means that as one variable increases, the other variable tends to decrease. The coefficient of determination (67.12%) represents the proportion of the total variation in the dependent variable that can be explained by the independent variable(s).

Explanation

The negative value of the correlation coefficient (-0.82) indicates a strong negative linear relationship between the variables in the data set. This means that as one variable increases, the other variable tends to decrease. The coefficient of determination (67.12%) represents the proportion of the total variation in the dependent variable that can be explained by the independent variable(s).

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21)

For the data set above, the Coefficient of Determination is 22.08%%. What is the Correlation Coefficient? (2 decimal places)

The negative correlation coefficient of -0.47 indicates a moderate negative linear relationship between the variables in the data set. This means that as one variable increases, the other variable tends to decrease. The coefficient of determination, which is the square of the correlation coefficient, tells us that 22.08% of the variation in one variable can be explained by the variation in the other variable.

Explanation

The negative correlation coefficient of -0.47 indicates a moderate negative linear relationship between the variables in the data set. This means that as one variable increases, the other variable tends to decrease. The coefficient of determination, which is the square of the correlation coefficient, tells us that 22.08% of the variation in one variable can be explained by the variation in the other variable.

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22)

For the data set above, the Coefficient of Determination is 50.04%. What is the Correlation Coefficient? (2 decimal places)

The Coefficient of Determination measures the proportion of the total variation in the dependent variable that can be explained by the independent variable(s). In this case, 50.04% of the total variation in the dependent variable can be explained by the independent variable(s). The Correlation Coefficient, on the other hand, measures the strength and direction of the linear relationship between two variables. Since the Coefficient of Determination is given, it implies that the square root of the Coefficient of Determination is equal to the Correlation Coefficient. Therefore, the Correlation Coefficient in this case is 0.71.

Explanation

The Coefficient of Determination measures the proportion of the total variation in the dependent variable that can be explained by the independent variable(s). In this case, 50.04% of the total variation in the dependent variable can be explained by the independent variable(s). The Correlation Coefficient, on the other hand, measures the strength and direction of the linear relationship between two variables. Since the Coefficient of Determination is given, it implies that the square root of the Coefficient of Determination is equal to the Correlation Coefficient. Therefore, the Correlation Coefficient in this case is 0.71.

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23)

For the data set above, the Coefficient of Determination is 26.70%. What is the Correlation Coefficient? (2 decimal places)

The coefficient of determination is a measure of how well the regression line fits the data points. It represents the proportion of the variance in the dependent variable that can be explained by the independent variable. In this case, the coefficient of determination is 26.70%, which means that 26.70% of the variance in the dependent variable can be explained by the independent variable. The correlation coefficient, on the other hand, measures the strength and direction of the linear relationship between the two variables. It ranges from -1 to 1, with 1 indicating a perfect positive linear relationship, 0 indicating no linear relationship, and -1 indicating a perfect negative linear relationship. Since the coefficient of determination is not the same as the correlation coefficient, we cannot directly determine the correlation coefficient from the given information. Therefore, the answer of 0.52 is not supported by the given data.

Explanation

The coefficient of determination is a measure of how well the regression line fits the data points. It represents the proportion of the variance in the dependent variable that can be explained by the independent variable. In this case, the coefficient of determination is 26.70%, which means that 26.70% of the variance in the dependent variable can be explained by the independent variable. The correlation coefficient, on the other hand, measures the strength and direction of the linear relationship between the two variables. It ranges from -1 to 1, with 1 indicating a perfect positive linear relationship, 0 indicating no linear relationship, and -1 indicating a perfect negative linear relationship. Since the coefficient of determination is not the same as the correlation coefficient, we cannot directly determine the correlation coefficient from the given information. Therefore, the answer of 0.52 is not supported by the given data.

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24)

For the data set above, the Coefficient of Determination is 44.88%. What is the Correlation Coefficient? (2 decimal places)

The coefficient of determination measures the proportion of the variation in the dependent variable that can be explained by the independent variable(s). In this case, 44.88% of the variation in the dependent variable can be explained by the independent variable(s). The correlation coefficient, on the other hand, measures the strength and direction of the linear relationship between two variables. Since the coefficient of determination is given, we can infer that the correlation coefficient is the square root of the coefficient of determination, which is approximately 0.67.

Explanation

The coefficient of determination measures the proportion of the variation in the dependent variable that can be explained by the independent variable(s). In this case, 44.88% of the variation in the dependent variable can be explained by the independent variable(s). The correlation coefficient, on the other hand, measures the strength and direction of the linear relationship between two variables. Since the coefficient of determination is given, we can infer that the correlation coefficient is the square root of the coefficient of determination, which is approximately 0.67.

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25)

For the data set above (Data 1), what is the value of 'r'? (3 decimal places)

The value of 'r' for the given data set is 0.996.

Explanation

The value of 'r' for the given data set is 0.996.

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29)

For the data set above (Data 4), what is the value of 'r'? (3 decimal places)

The value of 'r' for the given data set (Data 4) is 0.248.

Explanation

The value of 'r' for the given data set (Data 4) is 0.248.

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30)

For the data set above (Data 7 ), what is the value of 'r'? (1 decimal )

The value of 'r' is -0.7. This indicates a strong negative correlation between the variables in the data set. A correlation coefficient of -0.7 suggests that as one variable increases, the other variable tends to decrease, and vice versa.

Explanation

The value of 'r' is -0.7. This indicates a strong negative correlation between the variables in the data set. A correlation coefficient of -0.7 suggests that as one variable increases, the other variable tends to decrease, and vice versa.

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31)

For the data set above (Data 6 ), what is the value of 'r'? (3 decimal places)

The value of 'r' for the given data set is 0.803.

Explanation

The value of 'r' for the given data set is 0.803.

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32)

For the data set above (Data 8 ), what is the value of 'r'? (3 decimal places)

The value of 'r' for the given data set is 0.724.

Explanation

The value of 'r' for the given data set is 0.724.

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33)

For the data set above (Data 8 ), what is the value of 'r'? (2 decimal places)

The value of 'r' for the given data set is 0.72.

Explanation

The value of 'r' for the given data set is 0.72.

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34)

For the data set above (Data 10 ), what is the value of 'r'? (3 decimal places)

The value of 'r' for the given data set is 0.997.

Explanation

The value of 'r' for the given data set is 0.997.

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35)

For the data set above (Data 1), what is the value of the Correlation Coefficient? (3 decimal places)

The value of the correlation coefficient is 0.996. This indicates a strong positive linear relationship between the variables in the data set. A correlation coefficient of 0.996 suggests that there is a very high degree of correlation between the variables, meaning that as one variable increases, the other variable tends to increase as well.

Explanation

The value of the correlation coefficient is 0.996. This indicates a strong positive linear relationship between the variables in the data set. A correlation coefficient of 0.996 suggests that there is a very high degree of correlation between the variables, meaning that as one variable increases, the other variable tends to increase as well.

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36)

For the data set above (Data 2), what is the value of the Correlation Coefficient? (2 decimal places)

The value of the correlation coefficient measures the strength and direction of the linear relationship between two variables. A correlation coefficient of 0.93 indicates a strong positive linear relationship between the variables in the data set. This means that as one variable increases, the other variable also tends to increase. The value of 0.93 suggests a relatively strong and positive linear association between the variables.

Explanation

The value of the correlation coefficient measures the strength and direction of the linear relationship between two variables. A correlation coefficient of 0.93 indicates a strong positive linear relationship between the variables in the data set. This means that as one variable increases, the other variable also tends to increase. The value of 0.93 suggests a relatively strong and positive linear association between the variables.

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37)

For the data set above (Data 3), what is the value of the Correlation Coefficient? (3 decimal places)

The value of the correlation coefficient is -0.925. This indicates a strong negative linear relationship between the variables in the data set. As the correlation coefficient approaches -1, it suggests that as one variable increases, the other variable decreases in a consistent manner. In this case, the correlation coefficient of -0.925 suggests a strong negative relationship between the variables in the data set.

Explanation

The value of the correlation coefficient is -0.925. This indicates a strong negative linear relationship between the variables in the data set. As the correlation coefficient approaches -1, it suggests that as one variable increases, the other variable decreases in a consistent manner. In this case, the correlation coefficient of -0.925 suggests a strong negative relationship between the variables in the data set.

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38)

For the data set above (Data 4), what is the value of the Correlation Coefficient? (3 decimal places)

The value of the correlation coefficient is 0.248. This indicates a weak positive correlation between the variables in the data set.

Explanation

The value of the correlation coefficient is 0.248. This indicates a weak positive correlation between the variables in the data set.

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39)

For the data set above (Data 5 ), what is the value of the Correlation Coefficient? (2 decimal places)

The value of the correlation coefficient is 0.71. The correlation coefficient measures the strength and direction of the linear relationship between two variables. A value of 0.71 indicates a strong positive correlation, meaning that as one variable increases, the other variable tends to increase as well.

Explanation

The value of the correlation coefficient is 0.71. The correlation coefficient measures the strength and direction of the linear relationship between two variables. A value of 0.71 indicates a strong positive correlation, meaning that as one variable increases, the other variable tends to increase as well.

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40)

For the data set above (Data 6 ), what is the value of the Correlation Coefficient? (3 decimal places)

The value of the correlation coefficient for the given data set is 0.803. The correlation coefficient measures the strength and direction of the linear relationship between two variables. A value of 0.803 indicates a strong positive correlation, meaning that as one variable increases, the other variable also tends to increase. The correlation coefficient ranges from -1 to 1, where -1 represents a strong negative correlation and 1 represents a strong positive correlation.

Explanation

The value of the correlation coefficient for the given data set is 0.803. The correlation coefficient measures the strength and direction of the linear relationship between two variables. A value of 0.803 indicates a strong positive correlation, meaning that as one variable increases, the other variable also tends to increase. The correlation coefficient ranges from -1 to 1, where -1 represents a strong negative correlation and 1 represents a strong positive correlation.

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41)

For the data set above (Data 7 ), what is the value of the Correlation Coefficient? (1 decimal )

The value of the correlation coefficient indicates the strength and direction of the linear relationship between two variables. In this case, a correlation coefficient of -0.7 suggests a strong negative linear relationship between the variables in the data set. This means that as one variable increases, the other variable tends to decrease.

Explanation

The value of the correlation coefficient indicates the strength and direction of the linear relationship between two variables. In this case, a correlation coefficient of -0.7 suggests a strong negative linear relationship between the variables in the data set. This means that as one variable increases, the other variable tends to decrease.

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42)

For the data set above (Data 8 ), what is the value of the Correlation Coefficient? (2 decimal places)

The value of the Correlation Coefficient for the given data set is 0.72. The Correlation Coefficient measures the strength and direction of the linear relationship between two variables. A value of 0.72 indicates a strong positive correlation, meaning that as one variable increases, the other variable tends to increase as well. The value of 0.72 also suggests that the relationship between the variables is fairly linear, with little scatter around the trend line.

Explanation

The value of the Correlation Coefficient for the given data set is 0.72. The Correlation Coefficient measures the strength and direction of the linear relationship between two variables. A value of 0.72 indicates a strong positive correlation, meaning that as one variable increases, the other variable tends to increase as well. The value of 0.72 also suggests that the relationship between the variables is fairly linear, with little scatter around the trend line.

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