Final answer:
Measures that summarize the fit of a sample regression equation include the correlation coefficient, coefficient of determination, standard error of the estimate, ANOVA, and residual analysis. The coefficient of determination, in particular, is crucial as it indicates how much variance in the dependent variable is explained by the model.
Step-by-step explanation:
To assess how well the sample regression equation fits the data, we look at several statistical measures:
- Correlation coefficient (r): Indicates the strength and direction of the linear relationship between two variables.
- Coefficient of determination (r²): Represents the proportion of the variance in the dependent variable that is predictable from the independent variable.
- Standard error of the estimate (SEE): Measures the standard deviation of the observed values from the regression line.
- Analysis of variance (ANOVA): Tests whether the regression equation is statistically significant by comparing the variance explained by the model to the total variance.
- Residual analysis: Examines the difference between observed values and predicted values to assess the model's validity.
These measures help determine the quality of the regression equation as a predictor. The higher the r² value, the better the model explains the variation in the data. The other measures assist in gauging how well the model fits the data points and if the relationship between variables is statistically significant.