CFA Level II - Stats
, CFA Level II - Stats
Outliers - Answer: Computed correlation coefficients, as well as other sample
statistics, may be affected by outliers. Outliers represent a few extreme values for
sample observations. Relative to the rest of the sample data, the value of an
outlier may be extraordinarily large or small. Outliers can result in apparent
statistical evidence that a significant relationship exists when, in fact, there is
none, or that there is no relationship when, in fact, there is a relationship.
Spurious Correlation - Answer: Spurious correlation refers to the appearance of a
causal linear relationship when, in fact, there is no relation. Certain data items
may be highly correlated purely by chance. For example, suppose that you
compute the correlation coefficient for historical stock prices and snowfall totals
in Minnesota and get a statistically significant relationship—especially for the
month of January. Obviously, there is no economic explanation for this
relationship, so this would be considered a spurious correlation
Nonlinear Relationships - Answer: Correlation measures the linear relationship
between two variables. That's why in the first panel of Figure 3 the data points lie
perfectly on a straight line when the two variables are perfectly positively
correlated. For example, Y = 6 - 3X is a linear relationship. However, two variables
could have a nonlinear relationship yet a zero correlation. Therefore, another
limitation of correlation analysis is that it does not capture strong nonlinear
relationships between variables.
, CFA Level II - Stats
test of significance for the CORRELATION coefficient - Answer: Assuming that the
two populations are normally distributed:
t = [correlation x sqrt(n -2)] / sqrt(1-correlation^2)
reject Null if +Tcritical< T or T< -Tcritical
(think of the normal distribution and if the calculated t value is in the tails)
IF YOU CANT REJECT NULL, WE CONCLUDE THAT THE CORRELATION BETWEEN v
AND y IS NOT SIGNIGICANTLY DIFFERENT AT WHATEVER SINIFICANCE LEVEL
simple linear regression - Answer: The purpose of simple linear regression is to
explain the variation in a DEPENDENT variable in terms of the variation in a single
INDEPEDENT variable. Here, the term "variation" is interpreted as the degree to
which a variable differs from its mean value. Don't confuse variation with
variance—they are related but are not the same.
dependent variable - Answer: •The dependent variable is the variable whose
variation is explained by the independent variable. We are interested in answering
the question, "What explains fluctuations in the dependent variable?" The
dependent variable is also referred to as the EXPLAINED variable, the
ENDOGENOUS variable, or the PREDICTED variable.
GOES ON Y AXIS
, CFA Level II - Stats
independent variable - Answer: •The independent variable is the variable used to
explain the variation of the dependent variable. The independent variable is also
referred to as the EXPLANATORY variable, the EXOGENOUS variable, or the
PREDICTING variable.
GOES ON X AXIS
Suppose that you want to predict stock returns with GDP growth. Which variable
is the independent variable? - Answer: Because GDP is going to be used as a
predictor of stock returns, stock returns are being explained by GDP. Hence, stock
returns are the dependent (explained) variable, and GDP is the independent
(explanatory) variable.
Assumptions of the linear regression
most of the major assumptions pertain to the regression model's residual term
(ε). - Answer: 1.A linear relationship exists between the dependent and the
independent variable.
2.The independent variable is uncorrelated with the residuals.
3.The expected value of the residual term is zero [E(ε) = 0].
4.The variance of the residual term is constant for all observations .
5.The residual term is independently distributed; that is, the residual for one
observation is not correlated with that of another observation
6.The residual term is normally distributed
, CFA Level II - Stats
Outliers - Answer: Computed correlation coefficients, as well as other sample
statistics, may be affected by outliers. Outliers represent a few extreme values for
sample observations. Relative to the rest of the sample data, the value of an
outlier may be extraordinarily large or small. Outliers can result in apparent
statistical evidence that a significant relationship exists when, in fact, there is
none, or that there is no relationship when, in fact, there is a relationship.
Spurious Correlation - Answer: Spurious correlation refers to the appearance of a
causal linear relationship when, in fact, there is no relation. Certain data items
may be highly correlated purely by chance. For example, suppose that you
compute the correlation coefficient for historical stock prices and snowfall totals
in Minnesota and get a statistically significant relationship—especially for the
month of January. Obviously, there is no economic explanation for this
relationship, so this would be considered a spurious correlation
Nonlinear Relationships - Answer: Correlation measures the linear relationship
between two variables. That's why in the first panel of Figure 3 the data points lie
perfectly on a straight line when the two variables are perfectly positively
correlated. For example, Y = 6 - 3X is a linear relationship. However, two variables
could have a nonlinear relationship yet a zero correlation. Therefore, another
limitation of correlation analysis is that it does not capture strong nonlinear
relationships between variables.
, CFA Level II - Stats
test of significance for the CORRELATION coefficient - Answer: Assuming that the
two populations are normally distributed:
t = [correlation x sqrt(n -2)] / sqrt(1-correlation^2)
reject Null if +Tcritical< T or T< -Tcritical
(think of the normal distribution and if the calculated t value is in the tails)
IF YOU CANT REJECT NULL, WE CONCLUDE THAT THE CORRELATION BETWEEN v
AND y IS NOT SIGNIGICANTLY DIFFERENT AT WHATEVER SINIFICANCE LEVEL
simple linear regression - Answer: The purpose of simple linear regression is to
explain the variation in a DEPENDENT variable in terms of the variation in a single
INDEPEDENT variable. Here, the term "variation" is interpreted as the degree to
which a variable differs from its mean value. Don't confuse variation with
variance—they are related but are not the same.
dependent variable - Answer: •The dependent variable is the variable whose
variation is explained by the independent variable. We are interested in answering
the question, "What explains fluctuations in the dependent variable?" The
dependent variable is also referred to as the EXPLAINED variable, the
ENDOGENOUS variable, or the PREDICTED variable.
GOES ON Y AXIS
, CFA Level II - Stats
independent variable - Answer: •The independent variable is the variable used to
explain the variation of the dependent variable. The independent variable is also
referred to as the EXPLANATORY variable, the EXOGENOUS variable, or the
PREDICTING variable.
GOES ON X AXIS
Suppose that you want to predict stock returns with GDP growth. Which variable
is the independent variable? - Answer: Because GDP is going to be used as a
predictor of stock returns, stock returns are being explained by GDP. Hence, stock
returns are the dependent (explained) variable, and GDP is the independent
(explanatory) variable.
Assumptions of the linear regression
most of the major assumptions pertain to the regression model's residual term
(ε). - Answer: 1.A linear relationship exists between the dependent and the
independent variable.
2.The independent variable is uncorrelated with the residuals.
3.The expected value of the residual term is zero [E(ε) = 0].
4.The variance of the residual term is constant for all observations .
5.The residual term is independently distributed; that is, the residual for one
observation is not correlated with that of another observation
6.The residual term is normally distributed
