Please enable JavaScript.

Coggle requires JavaScript to display documents.

Quantitative Methods: Reading #10: Simple Linear Regression - Coggle…

- - - - In simple, linear regression, the estimated intercept & slope, bo & b1, are such that the sum of the squared vertical distances from the observations to the fitted line is minimized
      - b1 = Covariance of Y and X / Variance of X
        = Cov (Y, X) / o^2 (x)
        = [r (y,x) * o (y)] / o (x)
      - bo = Y - b1 * X
        => tóm lại là thế vào công thức để ra
  - - - involves many observations of X and Y for the same time period. These observations could come from different companies, asset classes, investment funds, countries, or other entities, depending on the regression model
        vd: chiều ko gian: 1 biến, nhiều sự vật tại 1 thời điểm: giá, của nhiều cty, tại một thời điểm
    - - use many observations from different time periods for the same company, asset class, investment fund, country, or other entity, depending on the regression model
        vd: chiều thời gian: nhiều biến, 1 sự vật, tại nhiều thời điểm: giá của HPG tại nhiều thời điểm
  - - - The relationship between the dependent variable, Y, and the independent variable, X, is linear
    - - The variance of the regression residuals is the same for all observations.
        + se = constant
    - - The observations, pairs of Ys and Xs, are independt of one another. This implies the regression residuals are uncorrelated across observations.
        + Re = 0
    - - The regression residuals (ei) are normally distributed
- - - - Test hypothesis
        
        H0: b1 = 0
        H1: b1 # 0
      - Component of F-test statistic
        
        MSR = SSR
        
        MSE = SSE / (n - 2)
      - F-test statistics
        
        The F-statistic in regression analysis is one side, with the rejection region on the right side, because we are interested in whether the variation in Y explained (the numerator) is larger than the variation in Y unexplained (the denominator).
        => Reject H0 if: F-statistic > F-crtical
        
        F = MSR / MSE
        
        k: number of variables
        
        n : number of observaitons
        
        Degree of freedom of numerator: k ( = 1)
        
        Degree of freesom of denominator: n - k -1 = n - 2
        
        Vì ở CFA level I chỉ học Simple linear regression nên k (số biến độc lập) bằng 1
- - - - Standard error of the slope coefficient: