Correlation & Regression

Question 1

Assumptions of the classic normal linear regression model

Answer 1

A linear relation exists between the dependent and independent variables.
The independent variable is uncorrelated with the residuals.
The expected value of the error term is 0.
The variance of the error term is the same for all observations (homoskedasticity).
The error term is uncorrelated across observations.
The error term is normally distributed.

Question 2

Calculated t for correlation significance

Answer 2

t = [r*sqrt(n-2)] / sqrt(1-r^2)

Question 3

Limitations of regression analysis

Answer 3

Linear relationships can change over time (parameter instability).
Even if regression model accurately reflects the historical relationship between two variables, its usefulness in investment analysis will be limited if other market participants are also aware of and act on this evidence.
If assumptions underlying regression analysis do not hold, the interpretation and tests of hypotheses may not be valid (i.e., if data is heteroskedastic or exhibits autocorrelation)

Question 4

Limitations of correlation analysis

Answer 4

Outliers may influence the results of regression and the estimate of the correlation coefficient.
Spurious correlation - there may appear to be a relationship between 2 variables when, in fact, there is none.
Correlation only measures linear relationships.

Question 5

t-test to determine if a correlation coefficient is statistically significant

Answer 5

t = [ r * sqrt(n-2)] / sqrt(1 - r^2)

r is significant if the test statistic is less than -t critical or greater than t critical with n-2 df