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Estimation of model error variance

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When we consider income and food expenditures, all households with the same income are expected to spend different amounts on food. Consequently, the random error will have different values for these households. The variance measures the spread of these errors around the population regression line. Note that denotes the variance of errors for the population. However, usually is unknown. In such cases, it is estimated by , which is the standard deviation of errors for the sample data.

An estimator for the variance of the population model error is

Division by () instead of results because the simple regression model uses two estimated parameters, a and b, instead of one.

The formula for SSE is

If we introduce the following notations

where stands for “sums of squares”, then

.


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Читайте в этой же книге: Hypothesis test for correlation | Exercises | Spearman rank correlation | Exercises | The linear regression model | Least squares coefficient estimators | Least square procedure | Interpretation of a and b | Assumptions of the regression model | Exercises |
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The explanatory power of a linear regression equation| Exercises

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