Models with qualitative explanatory variables p216

Transcription

1 Models with qualitative explanatory variables p216 Example gen = 1 for female Row gpa hsm gen

2 gpa = hsm gen Constant hsm gen S = R-Sq = 19.1% R-Sq(adj) = 18.3% Regression Residual Error Total

3 If the qualitative variable had more than two levels (say, l levels) introduce l-1 dummy variables. Example Length = length of stay in hospital (days) Nnurses = Number of nurses Region : There are 4 regions: NC, NE, S and W Row length nnurses region NC NE S W NC S W NE NC S NC S NC S W NE S length = nnurses NC NE S Constant nnurses NC NE S S = R-Sq = 33.7% R-Sq(adj) = 31.3% Regression Residual Error Total

4 Predicted Values (at nnurses = 150, NC = 1, NE =0, S = 0) Fit StDev Fit 95.0% CI 95.0% PI ( 8.981, ) ( 6.350, ) MINITAB Commands 4

5 5

6 Example Row Blue Green Lemon Insects trapped Test whether some colors are more attractive than others to beetles. Insects trapped = Blue Green Lemon Constant Blue Green Lemon S = R-Sq = 82.1% R-Sq(adj) = 79.4% Regression Residual Error Total

7 A test for comparing nested models p231 Definition Two models are nested if one model contains all the terms of the second model and at least one additional term. The model with more terms is called the complete (or full) model. The model with fewer terms is called the reduced (or restricted) model. Example 4.10 p 223 (Data from Table 4.4 p214) Row wt distance cost wt*dist wt**2 diast** a) Fit a complete second order model. 7

8 cost = wt dist wt*dist wt** dist**2 Constant wt dist wt*dist wt** dist** S = R-Sq = 99.4% R-Sq(adj) = 99.2% Regression Residual Error Total Source DF Seq SS wt dist wt*dist wt** dist** Test the hypothesis that the terms wt**2 and dist**2 can be dropped from the model. 8

9 cost = wt distance wt*dist Constant wt distance wt*dist S = R-Sq = 98.5% R-Sq(adj) = 98.3% Regression Residual Error Total Ex 5.14, p270, 5.15, p271 9

10 Examples (STA221 Apr 98 Final Exam) Weight = Diameter diam**2 Constant Diameter diam** S = R-Sq = 99.9% R-Sq(adj) = 99.9% Regression Residual Error Total Source DF Seq SS Diameter diam** The test of significance for the contribution of the second order term in diameter has an F-value of (to the nearest 50) A) 7600 B) 5300 C) 2650 D) 600 E) 350 Weight = Diameter Height Constant Diameter Height S = R-Sq = 97.8% R-Sq(adj) = 97.4% Regression Residual Error Total

11 Weight = Diameter Height diam** ht**2 Constant Diameter Height diam** ht** S = R-Sq = 99.9% R-Sq(adj) = 99.9% Regression Residual Error Total Source DF Seq SS Diameter Height diam** ht** Residuals Versus Weight (response is Weight) Residual Weight

12 Residuals Versus Height (response is Weight) Residual Height Residuals Versus the Fitted Values (response is Weight) Residual Fitted Value Normal Probability Plot of the Residuals (response is Weight) 2 1 Normal Score Residual 12

13 Histogram of the Residuals (response is Weight) 4 3 Frequency Residual Weight = Diameter Height diam*ht Constant Diameter Height diam*ht S = R-Sq = 99.4% R-Sq(adj) = 99.2% Regression Residual Error Total ) Which of the following are true? I) If we test the extra contribution of both height and height squared to the model with only diameter and diameter squared, the calculated F-statistics would be lass than 2. II) If we test the extra contribution of adding both height squared and diameter squared to the to the first order model with just height and diameter, the calculated F-statistic is lass than 200 III) If we assume the appropriateness of the model with diameter, height and their product, we see that the effect on dry weight of an increase in diameter is not independent of the height of the trees. IV) Residual plots indicate problems with the second order model containing diameter, height and their respective squares. 13

14 -Sequential Sums of Squares Regression Analysis: cost versus wt, distance, wt*dist, wt**2, dist**2 cost = wt distance wt*dist wt** dist**2 Predictor Coef SE Coef T P Constant wt distance wt*dist wt** dist** S = R-Sq = 99.4% R-Sq(adj) = 99.2% Regression Residual Error Total Source DF Seq SS wt distance wt*dist wt** dist** Regression Analysis: cost versus wt cost = wt Predictor Coef SE Coef T P 14

15 Constant wt S = R-Sq = 59.8% R-Sq(adj) = 57.6% Regression Residual Error Total Regression Analysis: cost versus wt, distance cost = wt distance Predictor Coef SE Coef T P Constant wt distance S = R-Sq = 91.6% R-Sq(adj) = 90.6% Regression Residual Error Total Regression Analysis: cost versus wt, distance, wt*dist cost = wt distance wt*dist 15

16 Predictor Coef SE Coef T P Constant wt distance wt*dist S = R-Sq = 98.5% R-Sq(adj) = 98.3% Regression Residual Error Total Regression Analysis: cost versus wt, distance, wt*dist, wt**2 cost = wt distance wt*dist wt**2 Predictor Coef SE Coef T P Constant wt distance wt*dist wt** S = R-Sq = 99.4% R-Sq(adj) = 99.2% Regression Residual Error Total

17 Regression Analysis: cost versus wt, distance, wt*dist, wt**2, dist**2 cost = wt distance wt*dist wt** dist**2 Predictor Coef SE Coef T P Constant wt distance wt*dist wt** dist** S = R-Sq = 99.4% R-Sq(adj) = 99.2% Regression Residual Error Total