FRM Part I · FRM Exam Part I · Linear Regression
In a simple linear regression of Y on X with 25 observations, the total sum of squares (TSS) is 400 and the sum of squared residuals (SSR, residuals) is 100. What are the R-squared and the standard error of the regression (SER)?
R-squared is 0.75 and the SER is about 2.09. R-squared equals one minus residual sum of squares over total sum of squares. The SER is the square root of residual sum of squares divided by n minus 2, which is the square root of 100/23.
- AR-squared = 0.75; SER = 2.09Correct
- BR-squared = 0.25; SER = 2.09
- CR-squared = 0.75; SER = 2.00
- DR-squared = 0.75; SER = 4.17
Explanation
R-squared = 1 - 100/400 = 0.75. SER = sqrt(SSR/(n-2)) = sqrt(100/23) = sqrt(4.348) = 2.085, about 2.09. Dividing by n = 25 gives 2.00, which ignores the two estimated parameters. 4.17 is the variance, not the standard error.
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