Solved on Mar 28, 2024

Interpret the coefficient of determination r2=0.8744932359r^2 = 0.8744932359 and explain its meaning.

STEP 1

1. The coefficient of determination, denoted as r2r^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.
2. The value of r2r^2 ranges from 0 to 1, where 0 indicates that the model does not explain any of the variability of the response data around its mean, and 1 indicates that the model explains all the variability of the response data around its mean.
3. The value of r2r^2 is the square of the correlation coefficient rr, which measures the strength and direction of a linear relationship between two variables on a scatterplot.

STEP 2

1. Interpret the value of r2r^2 in the context of a regression model.
2. Relate the interpretation to the proportion of variance explained.
3. Discuss the implications of the given r2r^2 value on the model's explanatory power.

STEP 3

Interpret the given value of r2r^2 in the context of a regression model.
Given that r2=0.8744932359r^2 = 0.8744932359, this implies that approximately 87.45% of the variance in the dependent variable can be explained by the independent variable(s) in the model.

STEP 4

Relate this interpretation to the proportion of variance explained.
The value of r2r^2 indicates a high degree of correlation between the independent and dependent variables, suggesting that the regression model fits the data well.

STEP 5

Discuss the implications of the given r2r^2 value on the model's explanatory power.
An r2r^2 value of 0.8744932359 suggests that the model has strong predictive power, as it accounts for a large portion of the variance in the dependent variable. However, it also indicates that approximately 12.55% of the variance is not explained by the model, which could be due to other variables not included in the model or inherent variability in the data.
The interpretation of r2=0.8744932359r^2 = 0.8744932359 is that the regression model explains about 87.45% of the variability of the dependent variable around its mean, which indicates a strong relationship between the variables in the model. This high level of explained variance suggests that the model has good predictive power.

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