Chap 9. 상관분석과 회귀분석


9.2 Correlation
  • Def. The sample correlation coefficient for the n pairs (x_1, y_1), ..., (x_n, y_n) is
  • The population correlation coefficient \rho is a parameter or population characteristic, so we can use the sample correlation coefficient to make various inferences about \rho, In particular, r is a point estimate for \rho, and the corresponding estimator is
  • Procedure for Testing H_0 : \rhp=0


9.3 Simple Linear Regression Analysis
  • There exist parameters \alpha, \beta, and \sigma^2 such that for any fixed value of the independent variable x, the dependent variable is related to x through the model equation
    The quality \epsilon in the model equation is a random variable, assumed to be normally distributed with E(\epsilon)=0 and V(\epsilon)=\sigma^2.
  • More generally the variable whose value is fixed by the experimeter will be denoted by x and will be called the independent variable.
  • For fixed x the second variable will be random; we denote this random variable and its observed value by Y and y, respectively, and refer to it as the dependent variable.
  • The least squares estimates of the coefficients \alpha and \beta of the regression line are
  • The ith predicted value, denoted by \hat y_i, is \hat y_i = \hat \alpha + \hat \beta x_i(i=1,...,n), and the ith residual is y_i - \hat y_i.
  • The error sum of squares, denoted by SSE, and the estimate of \sigma^2 is
  • The coefficient of determination denoted by \rho^2, is given by
  • The total sum of squares

  • coefficient of determination (회귀직선의 기여율)



9.4 Inferences about the Simple Linear Regression
  • \beta : population regression coefficient (모회귀계수)

  • 평균반응 \alpha+\beta x 에 관한 추론

  • 절편 \alpha에 관한 추론



9.5 Analysis of residuals
  • 표준화된 잔차인 \hat e_i,s = (y_i - \hat y_i) / \hat sigma들이 마치 표준정규분포 에서의 n개의 서로 독립인 관측값과 유사하게 나타나는가를 검토한다.

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