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The arm span and foot length were both measured (in centimeters) for each of 20 students in a biology class. The computer output displays the regression analysis.

Which of the following is the coefficient of determination?
0.63
0.65
0.79
0.81

2 Answers

5 votes

Final answer:

The coefficient of determination, denoted as r², is the proportion of variance in a dependent variable explained by an independent variable in a regression model. Without the value of r, we cannot identify the coefficient of determination from the options provided.

Step-by-step explanation:

The coefficient of determination 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. It is denoted as r² and is essentially the square of the correlation coefficient (r). In the context of your question from a biology class studying arm span and foot length, we would need to determine which of the provided values (0.63, 0.65, 0.79, 0.81) represents r². However, without the value of r, or additional context indicating which value is the result of squaring the correlation coefficient, we cannot directly identify the coefficient of determination from the options provided. Normally, you would square the correlation coefficient (for example, if r was 0.8, r² would be 0.64) to get the coefficient of determination.

The value of r² tells you the percentage of variance in the dependent variable explained by the independent variable, with the remainder (1 - r²) being unexplained variance.

User Javier Dottori
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The coefficient of determination, denoted as R^2, is a measure of how well the regression line fits the data points. It represents the proportion of the total variation in the dependent variable that is explained by the independent variable.

In the given scenario, we have a regression analysis output with arm span and foot length as the independent and dependent variables, respectively. To determine the coefficient of determination, we need to look for the R-squared value in the output.

Out of the given options, the coefficient of determination is 0.81.

Therefore, the answer is 0.81.
User Anjani
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