Solved on Mar 28, 2024
Interpret the coefficient of determination and explain its meaning.
STEP 1
1. The coefficient of determination, denoted as , 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 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 is the square of the correlation coefficient , which measures the strength and direction of a linear relationship between two variables on a scatterplot.
STEP 2
1. Interpret the value of in the context of a regression model.
2. Relate the interpretation to the proportion of variance explained.
3. Discuss the implications of the given value on the model's explanatory power.
STEP 3
Interpret the given value of in the context of a regression model.
Given that , 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 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 value on the model's explanatory power.
An 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 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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