Reading 11: Quantitative Methods Flashcards
Calculate and Interpret a sample covariance and a sample correlation coefficient, and interpret a scatter plot
Done.
Describe limitations to correlation analysis:
- Outliers: few extreme observations
- Spurious correlation: no causal relationship
- Non-linear relationships: can only measure linear relationships
Formulate a test of hypothesis that the population correlation coefficient equals zero, and determine whehter the hypothesis is rejected at a given significance.
Ho: Correlation = 0
H1: Correlation is not equal to 0
**REVIEW THE t-test formula
Distinguish between the dependent and independent variables in a linear regression.
- Dependent Variable: (“Y”) explained variable
- Independent Variable: (“X) explains the variation in the independent variable
Describe the assumptions underlying linear regression, and interpret regression coefficients.
Assumptions underlying linear regression:
- There IS a linear relationship
- Independent (“X”) variable uncorrelated with error term
- Expected value of error term is zero
- Variance of the error term is constant
- Error term is independently AND normally distributed
Calculate and Interpret the standard error of estimate, the coefficient of determination, and a confidence interval for a regression coefficient.
- Standard error of estimate (SEE): square root of MSE from ANOVA table
- Coefficeient of determination:
- Confidence interval: Point estimate +- (reliability x variabilty)
Formulate a null and alternative hypothesis about a population value of a regression coefficient, and determine the appropriate test statistic and whether the null hypothesis is rejected at a given significance.
See later definition.
Calculate the predicted value for the dependent variable, given an estimated regression model and a value for the independent variable.
Plug into the equation. Residual equlas the difference between predicted and actual.
Calculate and interpret a confidence interval for the predicted value of the dependent variable.
Predicted (“Y”) +- (t x standard error of forecast)
Critical t is two-tailed with n-2 degrees of freedom
Describe the use of analysis of variance (ANOVA) in regression analysis, interpret ANOVA results, and calculate and interpret the F-statistic.
- ANOVA: Refer to formula sheet table and definitions
- F-Statistic:
Explain limitations of regression analysis:
Limitations of regression analysis:
- Relationships change over time
- Assumptions are difficult to apply
- Usefullness limited for investment applications because everyone can observe the relationships