Financial Modelling M7&8

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jordan_hs
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287431
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Financial Modelling M7&8
Updated:
2014-10-29 09:14:22
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Regression M7
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  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
  17. Adjusted R2
    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

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