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CFA Level II Quantitative Methods > Reading 11 - Correlation and Regression > Flashcards

Reading 11 - Correlation and Regression Flashcards

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1
Q

In basic terms, what does covariance measure?

A

The degree to which two random variables move together

+ means they move together

  • means they move in opposite directions
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2
Q

What is the formula to calculate a sample covariance?

A
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3
Q

Why is the correlation coefficient a better statistical measure than sample variance?

A

B/c is converts the covariance into a standardized measure that is easier to interpret

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4
Q

What is Spurious Correlation?

A

the appearance of a causal linear relationship when, in fact, there is no relation

**May suggest investment strategies that appear profitable but actually would not be**

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5
Q

How do you calculate a sample correlation coefficient for securities X and Y (rXY) ?

A
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6
Q

How do you calculate the test statistic(used in a t-test) for the level of significance when given correlation (r) as your data point?

A
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7
Q

What are the underlying assumptions in a linear regression?

A
  1. A linear relationship exists between the dependent and independent variables
  2. The independent variable is uncorrelated with the residual return
  3. The expected value of the residual term is 0
  4. There is a constant variance of the residual term
  5. The residual term is independently distributed
  6. The residual term is normally distributed
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8
Q

What is the sum of squared errors (SSE) ?

& how is it calculated?

A

The sum of the squared vertical differences between the estimated and actual Y-values

****The regression line is the line that minimizes the SSE

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9
Q

How do you calculate the slope term

A

is equal to the covariance divided by

variance

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10
Q

How do you calculate the intercept term?

A

y - bar = mean of Y

x- bar = mean of X

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11
Q

What is the standard error of estimate (SEE)?

A

the degree of variability of the actual Y-values relative to the estimated Y-values from a regression equation

**SEE gauges the “fit” of the regression line

*** The smaller standard error the better, means the relationship is very strong

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12
Q

What is the coeffficient of determination (R2) ?

A

The percentage of the total variation in the dependent variable explained by the independent variable.

***R2 can be computed by simply squaring the correlation coeffcient

R2 = r2

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13
Q

What is the formula for the confidence interval for the regression coefficient (b1 hat)?

A
  • b1 hat is the estimated slope coefficient (ie beta)
  • tc is the two-tailed test statistic found in the back of the book
  • Sb1 is the standard error of the regression coefficient. This is almost always given in the problem
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14
Q

What is the formula when using a t-test to test the hypothesis that the true slope coefficient, b1, is equal to some hypothesized value ?

A

sb1 hat= standard error of the regression coefficient… will be given in the problem.

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15
Q

What are predicted values in an estimated regression model?

A

Are values of the dependent variable based on the estimated regression coefficients and a prediction about the independent variable.

***They are the values predicted by the regression equation

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16
Q

What is Analysis of variance (ANOVA) ?

A

A statistical procedure for analyzing the total variability of the dependent variable

17
Q

What does the Regression sum of squares (RSS) measure?

& how is it calculated???

A

It measures the variation in the dependent variable that is explained by the independent variable

18
Q

What does the Sum of squared errors (SSE) measure?

A

It measures the unexplained variation in the dependent variable

19
Q

How do we calculate the Total Variation in the dependent variable (SST)?

A

= explained variation + unexplained variation

or

SST = RSS + SSE

** = the sum of the squared differences between the actual Y values and the mean of Y

20
Q

What does an ANOVA table look like, describe it ….

A
21
Q

What is the formula to calculate R2 directly from the ANOVA table??

A
22
Q

What is the formula to calculate the standard error of estimate(SEE) directly from the ANOVA table??

A
23
Q

What is the difference between the sum of squared errors (SSE) and the standard error of estimate (SEE) ?

A

SSE is the sum of the squared residuals

SEE is the standard deviation of the residuals

24
Q

What does the F-statistic tell us?

A

How well a set of independent variables, as a group, explains the variation in the dependent variable

25
Q

What is the one critical thing to remember of the F-statistic?

A

It is always a one-tailed test !!

26
Q

What is the formula to calculate the F-statistic?

A
27
Q

Why is the F-test not as useful when we only have one independent variable?

A

B/c it tells us the same thing as the t-test of the slope coefficient

28
Q

What are the limitations to regression analysis?

A
  1. Linear relationships can change over time, meaning the equation may not be relevant for future forecasts (parameter instability)
  2. Even if the model is accurate, its usefulness in investment analysis will be limited if other market participants are also aware of it
  3. If the assumptions underlying regression analysis do not hold, the interpretation and tests of hypotheses may not be valid.
29
Q

Given two variables X and Y, what are the steps to calculate covariance between the two?

A
  1. Calculate the average of X of all times periods (X bar)
  2. Calculate the difference between X and X bar for each observation
  3. Repeat step 1-2 for Y
  4. Multiply (X-X bar)(Y-Y bar) and then sum all of the observations *** this is the top of the covar equation
  5. For the bottom, use # of obs - 1
30
Q

Given two variables X and Y, what are the steps to calculate the correlation coefficient between the two?

A
  1. Calculate the covariance
  2. Calculate the standard deviation for X and Y
  3. The variance is calculated by using the sum of (X-X bar)2 of the observations, then dividing by the # of obs - 1
  4. To get standard dev just take the square root of each
  5. The top of the equation is the covariance | the bottom is the standard dev of X & Y multiplied by each other
31
Q

What does this symbol represent?

A

The estimated intercept term. Where the regression line crosses the Y axis at x = 0

32
Q

What does this symbol represent ?

A

The slope of the regression line

Is equal to covariance / variance

33
Q

How many degrees of freedom (df) are used in a t-test?

A

n-2

34
Q

How do you determine whether an independent variable(s) are statistically significant?

A
  1. Perform a t-test
  2. t = the coefficient estimate / standard error of the coefficient
  3. **This is a two tailed test
  4. Find the critical value by looking it up under the table using n-k-1 degrees of freedom (n=obs, k = # of independent variables)
  5. If the absolute value of the test statistic is greater than the critical value they are significantly significant
35
Q

The **Standard Error of Estimate (SEE) **is also called two other names, what are they?

A
  1. Standard error of the residual
  2. Standard error of the regression

CFA Level II Quantitative Methods (3 decks)

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