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Load data set 111.
Which transformation has the highest correlation coefficient.
Correct Answer
A. X squared
Explanation
The transformation that has the highest correlation coefficient is x squared. This means that when the data set is transformed by squaring the x-values, it shows the strongest linear relationship with the y-values. The correlation coefficient measures the strength and direction of the linear relationship between two variables, with values ranging from -1 to 1. A correlation coefficient of 1 indicates a perfect positive linear relationship, meaning that as one variable increases, the other also increases in a consistent manner. Therefore, squaring the x-values in this data set results in the highest correlation coefficient.
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Load data set 112.
Which transformation has the highest correlation coefficient.
Correct Answer
B. Y squared
Explanation
The transformation with the highest correlation coefficient is "y squared". This means that when we square the values of the y variable, it shows the strongest correlation with the other variables in the dataset. The squared transformation can help to capture non-linear relationships between variables and may be useful in cases where the relationship between y and the other variables is not linear.
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Load data set 121.
Which transformation has the highest correlation coefficient.
Correct Answer
B. Y squared
Explanation
The transformation with the highest correlation coefficient is "y squared." This means that the dependent variable, y, is squared. The correlation coefficient measures the strength and direction of the linear relationship between two variables. By squaring y, we are potentially capturing a stronger relationship between the variables, resulting in a higher correlation coefficient.
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Load data set 122.
Which transformation has the highest correlation coefficient.
Correct Answer
E. Log x
Explanation
The transformation with the highest correlation coefficient is "log x." This means that taking the logarithm of the x values in the data set will result in the highest correlation coefficient when compared to the y values. This suggests that there is a strong relationship between the logarithm of the x values and the y values in the data set.
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Load data set 123.Which transformation has the highest correlation coefficient.
Correct Answer
C. 1/x
Explanation
The transformation 1/x has the highest correlation coefficient because it transforms the data in a way that maximizes the correlation between the variables. This transformation is commonly used when dealing with data that has a non-linear relationship, as it can help to linearize the relationship and improve the correlation. By taking the reciprocal of each x value, the resulting values will be larger for smaller x values and smaller for larger x values, which can help to better capture the relationship between the variables.
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Load data set 131.
Which transformation has the highest correlation coefficient.
Correct Answer
E. Log x
Explanation
The transformation with the highest correlation coefficient is "log x". This means that taking the logarithm of the x-values in the data set has the strongest positive linear relationship with the y-values. The logarithm transformation can help to linearize data that follows an exponential growth pattern, making it easier to analyze and interpret the relationship between the variables.
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Load data set 132.
Which transformation has the highest correlation coefficient.
Correct Answer
E. Log x
Explanation
The transformation "log x" has the highest correlation coefficient. This means that when the data set 132 is transformed using the logarithm function on the x-values, it will result in a higher correlation coefficient compared to the other transformations listed.
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Load data set 133.
Which transformation has the highest correlation coefficient.
Correct Answer
E. Log x
Explanation
The transformation with the highest correlation coefficient is "log x". This means that taking the logarithm of the variable x will result in a stronger correlation with the other variables in the dataset compared to the other transformations listed.
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Load data set 141.
Which transformation has the highest correlation coefficient.
Correct Answer
A. X squared
Explanation
The transformation with the highest correlation coefficient is x squared. This means that when the data set is transformed by squaring the x values, it will have the strongest linear relationship with the y values compared to the other transformations listed.
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Load data set 143.
Which transformation has the highest correlation coefficient.
Correct Answer
F. Log y
Explanation
The transformation "log y" has the highest correlation coefficient. This means that when the dependent variable (y) is transformed using the logarithm function, it shows a stronger linear relationship with the independent variable(s) in the data set 143 compared to other transformations such as x squared, y squared, 1/x, 1/y, or log x.
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From the data above, what is the correlation coefficient for the log x transformation? (4 decimal places)
Correct Answer
0.8814
Explanation
The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient for the log x transformation is 0.8814. This suggests a strong positive linear relationship between the variables. The value of 0.8814 indicates that as the log x value increases, the corresponding y value also tends to increase.
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From the data above, what is the correlation coefficient for the reciprocal x transformation? (4 decimal places)
Correct Answer
-0.6852
Explanation
The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient for the reciprocal x transformation is -0.6852. This means that there is a moderate negative linear relationship between the reciprocal of x and the other variable. As the value of the reciprocal of x increases, the other variable tends to decrease. The negative sign indicates the direction of the relationship, while the value of -0.6852 indicates the strength, with values closer to -1 indicating a stronger negative relationship.
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