"In Exercises 13-16, use the value of the correlation coefficient r to calculate the coefficient of determination r^2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation?
14.r =- 0.937"

검증된 단계별 안내

Identify the given correlation coefficient, which is

r = -0.937

Calculate the coefficient of determination by squaring the correlation coefficient:

r^2 = (-0.937)^2

. This value represents the proportion of the variance in the dependent variable that is predictable from the independent variable.

Interpret the coefficient of determination

r^2

as the explained variation, meaning the percentage of the total variation in the data that is explained by the regression line.

Calculate the unexplained variation by subtracting the coefficient of determination from 1:

1 - r^2

. This represents the proportion of the variation in the data that is not explained by the regression line.

Summarize the results by stating that a higher

r^2

value indicates a better fit of the regression line to the data, meaning more explained variation and less unexplained variation.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Correlation Coefficient (r)

The correlation coefficient, denoted as r, measures the strength and direction of a linear relationship between two variables. Its value ranges from -1 to 1, where values close to -1 or 1 indicate strong linear relationships, and values near 0 indicate weak or no linear relationship.

Coefficient of Determination (r²)

The coefficient of determination, r², is the square of the correlation coefficient and represents the proportion of the variance in the dependent variable explained by the independent variable. It ranges from 0 to 1, with higher values indicating a better fit of the regression line to the data.

Explained vs. Unexplained Variation

Explained variation refers to the portion of total variation in the data accounted for by the regression model, quantified by r². Unexplained variation is the remaining variation not captured by the model, representing random error or other factors affecting the dependent variable.

"In Exercises 13-16, use the value of the correlation coefficient r to calculate the coefficient of determination r^2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation?14.r =- 0.937"