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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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