Skip to main content
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 9.1.16
Capitolo 9, Problema 9.1.16

"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?
16. r = 0.795"

Guida verificata passo dopo passo
1
Identify the given correlation coefficient, which is r = 0.795.
Calculate the coefficient of determination by squaring the correlation coefficient: r2 = (0.795)^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 variation in the independent variable through the regression line.
Understand that the explained variation corresponds to r^2, while the unexplained variation corresponds to 1 - r^2, representing the variation not accounted for by the regression model.
Summarize that a higher r^2 value indicates a better fit of the regression line to the data, meaning more of the variation is explained, and less is unexplained.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
2m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

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 a strong linear relationship, and values near 0 indicate little to no linear association.
Video consigliato:
Percorso guidato
05:43
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. It ranges from 0 to 1, with higher values indicating a better fit of the regression line to the data.
Video consigliato:
Percorso guidato
06:14
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 outside the regression.
Video consigliato:
Percorso guidato
04:39
Visualizing Qualitative vs. Quantitative Data
Pratica correlata
Domanda del libro di testo

"In Exercises 19-22, two variables are given that have been shown to have correlation but no cause-and-effect relationship. Describe at least one possible reason for the correlation.

19. Value of home and life span"

59
views
Domanda del libro di testo

"Old Vehicles In Exercises 31–34, use the figure shown at the left.

Regression Line Find and draw the regression line."

37
views
Domanda del libro di testo

"Predicting y-Values In Exercises 3-6, use the multiple regression equation to predict the y-values for the values of the independent variables.

4. Sorghum Yield The equation used to predict the annual sorghum yield (in bushels per

acre) is y = 80.1-20.2x_1 +21.2x_2

where x_1 is the number of acres planted (in millions) and x_2 is the number of acres harvested (in millions). (Adapted from United States Department of Agriculture)

a. x_1 = 5.5, x_2 = 3.9

b. x_1 = 8.3, x_2 = 7.3

c. x_1 = 6.5, x_2 = 5.7

d. x_1 = 9.4, x_2= 7.8"

39
views