Business and Economic Statistics 2

Sec_16.3.pdf-Page 20 Section 16.3 Analysis of

25 Section 14.8-14.9 Residual Analysis  Residual for observation i i i y y ˆ  Note: It ’ s the error resulting from using the estimated regression equation to predict the value of the dependent variable. Example: i x i y i y ˆ i i y y ˆ  1 14 15 3 24 25 2 18 20 1 17 15 3 27 25  Assumptions about  1. The error  is a random variable with a mean of zero, 0 ) (   E . 2. The variance of 

STA | STA351 | Business and Economic Statistics 2 | 25 Section 14.8-14.9 Residual 

Page 25 Section 15.8 Residual Analysis  Residual Analysis  Recall, the residual for the i th observation is   −   .  The residuals provide the best information about  .  Residual Analysis : an analysis of the corresponding residuals for help in determining whether the assumptions made about the regression model and the error term  are appropriate.  If

STA | STA351 | Business and Economic Statistics 2 | Page 25 Section 15.8 Residual 

Page 9 Section 15.4 Model Assumptions Assumptions about the error term  in the multiple regression model            p p x x x y  2 2 1 1 0 1. The error term  is a random variable with a mean of zero. 2. The variance of  , denoted by 2  , is the same for all values of the independent variables  1 , 2 ,⋯,  . 3. The values of  are independent. 4. The error term  is a normall

STA | STA351 | Business and Economic Statistics 2 | Page 9 Section 15.4 Model Assu

Page 16 Section 15.6 Estimation and Prediction  Point Estimation - The procedures for estimating the mean value of y and predicting an individual value of y in multiple regression are similar to those in simple regression. - p p x b x b x b b y       2 2 1 1 0 ˆ is the point estimation in both cases.  Interval Estimation Confidence interval : an interval estimate of

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