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Ch. 9 - Correlation and Regression
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 9 - Correlation and RegressionProblema 9.3.7
Capitolo 9, Problema 9.3.7

"In Exercises 7-10, 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?
7. r =0.465"

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Identify the given correlation coefficient, which is r = 0.465.
Calculate the coefficient of determination by squaring the correlation coefficient: r2 = (0.465)^2. This value is denoted as r^2.
Interpret r^2 as the proportion of the total variation in the dependent variable that is explained by the independent variable through the regression line. It represents the explained variation.
Understand that the unexplained variation is the remaining proportion of the total variation, which can be found by subtracting r^2 from 1, i.e., 1 - r^2.
Summarize that a higher r^2 value indicates a better fit of the regression line to the data, meaning more variation is explained, while a lower r^2 means more variation remains unexplained.

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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 positive or negative linear relationships, respectively, and values near 0 indicate weak or no linear relationship.
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Correlation Coefficient

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 in a regression model. It ranges from 0 to 1, with higher values indicating a better fit of the regression line to the data.
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Coefficient of Determination

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. Together, they sum to the total variation in the dependent variable.
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Visualizing Qualitative vs. Quantitative Data
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