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Comment: Estimates and residuals
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| A regression line passes through two points: | Based on [[Econometrics/LinearRegression|regression]], the estimated outcome for observation ''i'' is: |
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| and | And the residual is: |
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| {{attachment:regression2.svg}} | {{attachment:residual.svg}} |
Econometrics Notation
Data
The number of observations is n.
The outcome variable is y. For observation i, the outcome value is yi.
The treatment variable is x1. For observation i, the treatment value is x1i.
The control variables are x2 through xk (up to k - 1 control variables). For observation i, a control value might be x2i.
Statistics
The average outcome is:
The variance is:
The standard deviation is:
The covariance between the treatment and outcome is:
The correlation between the treatment and outcome is:
Based on regression, the estimated outcome for observation i is:
And the residual is:
