Reading 11: Quantitative Methods

Question 1

Calculate and Interpret a sample covariance and a sample correlation coefficient, and interpret a scatter plot

Answer 1

Done.

Question 2

Describe limitations to correlation analysis:

Answer 2

1. Outliers: few extreme observations
2. Spurious correlation: no causal relationship
3. Non-linear relationships: can only measure linear relationships

Question 3

Formulate a test of hypothesis that the population correlation coefficient equals zero, and determine whehter the hypothesis is rejected at a given significance.

Answer 3

Ho: Correlation = 0

H1: Correlation is not equal to 0

**REVIEW THE t-test formula

Question 4

Distinguish between the dependent and independent variables in a linear regression.

Answer 4

• Dependent Variable: (“Y”) explained variable
• Independent Variable: (“X) explains the variation in the independent variable

Question 5

Describe the assumptions underlying linear regression, and interpret regression coefficients.

Answer 5

Assumptions underlying linear regression:

1. There IS a linear relationship
2. Independent (“X”) variable uncorrelated with error term
3. Expected value of error term is zero
4. Variance of the error term is constant
5. Error term is independently AND normally distributed

Question 6

Calculate and Interpret the standard error of estimate, the coefficient of determination, and a confidence interval for a regression coefficient.

Answer 6

• Standard error of estimate (SEE): square root of MSE from ANOVA table
• Coefficeient of determination:
• Confidence interval: Point estimate +- (reliability x variabilty)

Question 7

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.

Answer 7

See later definition.

Question 8

Calculate the predicted value for the dependent variable, given an estimated regression model and a value for the independent variable.

Answer 8

Plug into the equation. Residual equlas the difference between predicted and actual.

Question 9

Calculate and interpret a confidence interval for the predicted value of the dependent variable.

Answer 9

Predicted (“Y”) +- (t x standard error of forecast)

Critical t is two-tailed with n-2 degrees of freedom

Question 10

Describe the use of analysis of variance (ANOVA) in regression analysis, interpret ANOVA results, and calculate and interpret the F-statistic.

Answer 10

• ANOVA: Refer to formula sheet table and definitions
• F-Statistic:

Question 11

Explain limitations of regression analysis:

Answer 11

Limitations of regression analysis:

1. Relationships change over time
2. Assumptions are difficult to apply
3. Usefullness limited for investment applications because everyone can observe the relationships