Financial Modelling M7&8

Card Set Information

 Author: jordan_hs ID: 287431 Filename: Financial Modelling M7&8 Updated: 2014-10-29 13:14:22 Tags: Regression M7 Folders: Description: Show Answers:

Home > Flashcards > Print Preview

The flashcards below were created by user jordan_hs on FreezingBlue Flashcards. What would you like to do?

1. Regression analysis used to
• Predict the value of a dependent variable based on the value of at least one independent variable

• Explain the impact of changes in an independent variable on the dependent variable
2. The relationship between X and Y is described by a linear function
• • Dependent variable Y: the variable we wish to explain
• • Independent variable X: the variable used to explain the dependent variable
3. Linear regression population equation model

• Where:
•  = Dependent variable
•  = Intercept
•  = Slope Coefficient
•  = Independent Variable
•  = Random Error term
4. Linear Regression Model Assumptions
• - Linearity
• - Independence of errors
• - Normality of error
• - Equal Variance
5. Linear Regression Model Assumptions
- Linearity
States that the relationship between variables islinear
6. Linear Regression Model Assumptions
- Independence of errors
Requires that the errors are independent of one another. This assumption is particularly important when data are collected over a period of time.
7. Linear Regression Model Assumptions
- Normality of error
Requires that the errors are normallydistributed at each value of X
8. Linear Regression Model Assumptions
- Equal variance or homoscedasticity
Requires that the variance of the errors be constant for all values of X. In other words, the variability of Y values is the same when Xis a low value as when X is a high value.
9. The Coefficient of Correlation
• • The coefficient of correlation measures the relative strength of a linear relationship between two numerical variables.
• • The values of the coefficient of correlation range from for a perfect negative correlation (‐1) to for a perfect positive correlation (+1).
10. Correlation between X and Y
• Excel Correlation Output
• Data / data analysis / correlation

• Regression and Correlation are related ideas.
• • Correlation analysis is concern with knowing whether there is a relationship between X and Y.
• • Regression analysis is to predict the relationship between variables so as to find an approximate value of X from the value of Y
11. Linear Regression
- Regression using excel
Data / Data Analysis / Regression
12. Interpretation of the Intercept,
β0 is the estimated average value of Y when the value of X is zero (if X = 0 is in the range of observed X values)

example: No houses had 0 square feet, so β0 = 98.24833 just indicates that, for houses within the range of sizes observed, \$98,248.33 is the portion of the house price not explained by square feet
13. Interpretation of the Slope Coefficient,  β1
• β1 measures the estimated change in the average value of Y as a result of a one‐unit change in X

• Example:
• • β1 = 0.10977 tells us that the average value of a house increases by .10977(\$1000) = \$109.77, on average, for each additional one square foot of size
14. Coefficient of Determination, R2
• - Is the portion of the total variation in the dependent variable that is explained by variation in the independent
• - also called R-squared, R2
• - Indicates how well data points fit a statistical model

•  &
15. Ron excel
R Square figure and found via ANOVA with Regression divided by Total

e.g. 58.08% of variation in house price is explained by variation in square feet
16. When R2 = 1?
When 0 < R2 < 1
• R2=1
• Perfect linear relationship between x & y
• - Also 100% of variation in Y ix explained by variation in X

• 0<R2<1
• Weaker linear relationships between X and Y
• - Also some but not all of the variation in Y is explained by variation in X
An attempt to take account of the phenomenon of R2 automatically and spuriously increasing when extra explanatory variables are added to the model
18. Standard error
Measure of variation of observed y values from the regression line - the smaller the better

19. Interpret Excel output
- Whether to accept/reject null hypothesis
Check p-value of bottom row

depends of the significance level, if less than significance level, reject hypothesis
20. Residual plots
• Plot residuals on vertical axis against corresponding values of independent variables on horizontal axis (residuals vs independent variable).
• Evaluate linearity and constant variance assumptions
• If model is appropriate for data, WE WILL NOT SEE ANY APPARENT PATTERN IN PLOT
21. Normal Probability Plot
• Visual display that helps to evaluate whether data is normally distributed.
• If assumption is met, plot should look like a straight line

What would you like to do?

Home > Flashcards > Print Preview