Which statement about the coefficient of determination (R^2) is true?It represents the slope of the regression line.It indicates the percentage of the variance in the dependent variable that is predictable from the independent variable.It can take on any value between -1 and 1.It is the square root of the correlation coefficient.
Question
Which statement about the coefficient of determination (R^2) is true?It represents the slope of the regression line.It indicates the percentage of the variance in the dependent variable that is predictable from the independent variable.It can take on any value between -1 and 1.It is the square root of the correlation coefficient.
Solution
The true statement about the coefficient of determination (R^2) is: "It indicates the percentage of the variance in the dependent variable that is predictable from the independent variable."
Here's why:
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"It represents the slope of the regression line." - This is incorrect. The slope of the regression line is represented by the regression coefficient, not R^2.
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"It indicates the percentage of the variance in the dependent variable that is predictable from the independent variable." - This is correct. R^2 is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model.
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"It can take on any value between -1 and 1." - This is incorrect. R^2 ranges from 0 to 1. A negative R^2 does not make sense because it would mean that the model explains less than 0% of the variance, which is not possible.
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"It is the square root of the correlation coefficient." - This is incorrect. The square root of the correlation coefficient (r) is related to R^2, but they are not the same. R^2 is the square of the correlation coefficient, not the square root.
Similar Questions
When conducting a regression analysis, what does the coefficient of determination (R-squared) represent? A. The strength of the relationship between variables B. The predicted values of the dependent variable C. The slope of the regression line D. The proportion of variance in the dependent variable explained by the independent variable
The coefficient of determination, r2, represents:Group of answer choicesDirection and strength of a correlationProbability that the data resulted by random chanceThe amount of skew in a distributionThe amount that data deviate from the mean valueThe proportion of total variation explained by a linear correlation
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How do you interpret a coefficient of determination, r², equal to 0.14? Choose the correct answer below. A The interpretation is that 86% of the variation in the independent variable can be explained by the variation in the dependent variable. OB. The interpretation is that 0.14% of the variation in the independent variable can be explained by the variation in the dependent variable. OC. The interpretation is that 0.86% of the variation in the dependent variable can be explained by the variation in the independent variable. OD. The interpretation is that 14% of the variation in the dependent variable can be explained by the variation in the independent variable.
Select all correct statements regarding the coefficient of determination from below.Question 5AnswerSelect one or more:a.When it is close to zero, it means the predictor X is not related to Y.b.It measures the proportion of variation in Y that can be explained by the fitted linear regression model.c.In simple linear regression, it measures the degree of linear relationship between X and Y.d.It is equal to , where is the sample correlation coefficient of X and Y.
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