CFA Level II: Formulas Questions And
Answers With Verified Solutions 100%
Correct!!!
Slope Coefficient (b̂1) for the Regression Line - ANSWER✔✔Describes the
change in Y for a one-unit change in X. It can be positive, negative, or zero,
depending on the relationship between the regression variables. The slope term is
calculated as:
b̂1 = Cov(xy)/(σ^2)x
Durbin-Watson (DW) Statistic - ANSWER✔✔DW = ∑t =
2T(ε^t−ε^t−1)2∑t=1Tε^t2
OR, if the sample size is very large:
**DW ≈ 2(1 − ρ)**-->This is more likely on test
Where:
ε^t = residual for period t
ρ = correlation coefficient between residuals from one period and those from the
previous period
-DW ≈ 2 if the error terms are homoskedastistic and not serially correlated (ρ = 0)
-DW < 2 if the error terms are POSITIVELY serially correlated (ρ > 0)
-DW > 2 if the error terms are NEGATIVELY serially correlated (ρ < 0)
,Test Procedure for Positive Serial Correlation:
-H0: the regression has no positive serial correlation
-->If DW < dl, the error terms are positively serially correlated (i.e., reject the null
hypothesis of no positive serial correlation).
-->If dl < DW < du, the test is inconclusive.
-->If DW > du, there is no evidence that the error terms are positively correlated.
(i.e., fail to reject the null of no positive serial correlation).
Where:
dl = Lower Critical DW value
du = Upper Critical DW Value
**Remember: Cannot use DW to test for Serial Correlation in an AR model
Total Sum of Squares (SST) - ANSWER✔✔Measures the total variation in the
dependent variable. SST is equal to the sum of the squared differences between the
actual Y-values and the mean of Y (Ȳ).
SST = ∑(Yi−Ȳ)^2
Where:
Ȳ = Mean of Y
Remember:
SST = RSS + SSE
,Regression Sum of Squares (RSS) - ANSWER✔✔Measures the variation in the
dependent variable that is explained by the independent variable. RSS is the sum of
the squared distances between the predicted Y-values and the mean of Y.
This is the "explained" portion of the variation of the dependent variable
RSS = ∑(Ŷi−Ȳ)^2
Where:
Ŷ = Predicted Y-Values
Ȳ = Mean of Y
Sum of Squared Errors (SSE) - ANSWER✔✔Measures the unexplained variation
in the dependent variable that is explained by the independent variable; The sum of
squared vertical distances between estimated and actual Y-values
The sum of the squared vertical distances between the estimated and actual Y-
values (when drawing a regression line) is referred to as the sum of squared errors
(SSE)
Measures the UNEXPLAINED variation in the dependent variable. It's also known
as the sum of squared residuals or the residual sum of squares. SSE is the sum of
the squared vertical distances between the actual Y-values and the predicted Y-
values on the regression line.
The sum of squared residuals.
, Regression lines minimize the SSE measure for a given scatter plot of data.
SSE = ∑(Yi−Ŷ)^2
Where:
Ŷ = Predicted Y-Values
Total Variation (SST) - ANSWER✔✔Total Variation = Explained Variation +
Unexplained Variation
or
SST = RSS + SSE
Standard Error of Estimate (SEE) - ANSWER✔✔The Standard Error of Estimate
(SEE) for a regression is the standard deviation of its residuals. SEE measure
accuracy of predicted values from regression equation.
Remember: The lower the SEE, the better the model fit. In this way, SEE is a
metric of quality of model fit.
Remember: A LOW SEE implies a HIGH R^2
SEE = (MSE)^(1/2) = ((SSE/(n-k-1))^(1/2)
MSE = Mean Squared Error = (1/n)(∑(Yi−Ŷ)^2)
Answers With Verified Solutions 100%
Correct!!!
Slope Coefficient (b̂1) for the Regression Line - ANSWER✔✔Describes the
change in Y for a one-unit change in X. It can be positive, negative, or zero,
depending on the relationship between the regression variables. The slope term is
calculated as:
b̂1 = Cov(xy)/(σ^2)x
Durbin-Watson (DW) Statistic - ANSWER✔✔DW = ∑t =
2T(ε^t−ε^t−1)2∑t=1Tε^t2
OR, if the sample size is very large:
**DW ≈ 2(1 − ρ)**-->This is more likely on test
Where:
ε^t = residual for period t
ρ = correlation coefficient between residuals from one period and those from the
previous period
-DW ≈ 2 if the error terms are homoskedastistic and not serially correlated (ρ = 0)
-DW < 2 if the error terms are POSITIVELY serially correlated (ρ > 0)
-DW > 2 if the error terms are NEGATIVELY serially correlated (ρ < 0)
,Test Procedure for Positive Serial Correlation:
-H0: the regression has no positive serial correlation
-->If DW < dl, the error terms are positively serially correlated (i.e., reject the null
hypothesis of no positive serial correlation).
-->If dl < DW < du, the test is inconclusive.
-->If DW > du, there is no evidence that the error terms are positively correlated.
(i.e., fail to reject the null of no positive serial correlation).
Where:
dl = Lower Critical DW value
du = Upper Critical DW Value
**Remember: Cannot use DW to test for Serial Correlation in an AR model
Total Sum of Squares (SST) - ANSWER✔✔Measures the total variation in the
dependent variable. SST is equal to the sum of the squared differences between the
actual Y-values and the mean of Y (Ȳ).
SST = ∑(Yi−Ȳ)^2
Where:
Ȳ = Mean of Y
Remember:
SST = RSS + SSE
,Regression Sum of Squares (RSS) - ANSWER✔✔Measures the variation in the
dependent variable that is explained by the independent variable. RSS is the sum of
the squared distances between the predicted Y-values and the mean of Y.
This is the "explained" portion of the variation of the dependent variable
RSS = ∑(Ŷi−Ȳ)^2
Where:
Ŷ = Predicted Y-Values
Ȳ = Mean of Y
Sum of Squared Errors (SSE) - ANSWER✔✔Measures the unexplained variation
in the dependent variable that is explained by the independent variable; The sum of
squared vertical distances between estimated and actual Y-values
The sum of the squared vertical distances between the estimated and actual Y-
values (when drawing a regression line) is referred to as the sum of squared errors
(SSE)
Measures the UNEXPLAINED variation in the dependent variable. It's also known
as the sum of squared residuals or the residual sum of squares. SSE is the sum of
the squared vertical distances between the actual Y-values and the predicted Y-
values on the regression line.
The sum of squared residuals.
, Regression lines minimize the SSE measure for a given scatter plot of data.
SSE = ∑(Yi−Ŷ)^2
Where:
Ŷ = Predicted Y-Values
Total Variation (SST) - ANSWER✔✔Total Variation = Explained Variation +
Unexplained Variation
or
SST = RSS + SSE
Standard Error of Estimate (SEE) - ANSWER✔✔The Standard Error of Estimate
(SEE) for a regression is the standard deviation of its residuals. SEE measure
accuracy of predicted values from regression equation.
Remember: The lower the SEE, the better the model fit. In this way, SEE is a
metric of quality of model fit.
Remember: A LOW SEE implies a HIGH R^2
SEE = (MSE)^(1/2) = ((SSE/(n-k-1))^(1/2)
MSE = Mean Squared Error = (1/n)(∑(Yi−Ŷ)^2)
