Preparatory Computations

252y0541s 5/7/05

ECO252 QBA2, Final EXAM, May 4, 2005

Preparatory Computations

Part I Regression problem.

————— 4/28/2005 6:18:32 PM ————————————————————

Welcome to Minitab, press F1 for help.

Results for: 252x0504-4.MTW

MTB > Stepwise 'MPG' 'Horsepower' 'Length' 'Width' 'Weight' 'Cargo Volume' &

CONT> 'Turning Circle' 'SUV_D' 'Fuel_D' 'SUVwt' 'HPsq' 'AWD_D' &

CONT> 'FWD_D' 'RWD_D' 'SUV_L';

SUBC> AEnter 0.15;

SUBC> ARemove 0.15;

SUBC> Best 0;

SUBC> Constant.

Stepwise Regression: MPG versus Horsepower, Length, ...

Alpha-to-Enter: 0.15 Alpha-to-Remove: 0.15

Response is MPG on 14 predictors, with N = 119

N(cases with missing observations) = 2 N(all cases) = 121

Step 1 2 3 4 5 6

Constant 38.31 36.75 41.59 50.06 50.15 59.00

Weight -0.00491 -0.00436 -0.00578 -0.00495 -0.00424 -0.00339

T-Value -15.34 -11.87 -12.82 -9.31 -6.74 -5.61

P-Value 0.000 0.000 0.000 0.000 0.000 0.000

SUV_D -1.72 -33.71 -35.29 -35.12 -18.68

T-Value -2.84 -4.99 -5.36 -5.40 -2.71

P-Value 0.005 0.000 0.000 0.000 0.008

SUV_L 0.180 0.185 0.182 0.088

T-Value 4.75 5.04 5.01 2.26

P-Value 0.000 0.000 0.000 0.026

Turning Circle -0.285 -0.292 -0.255

T-Value -2.79 -2.90 -2.75

P-Value 0.006 0.004 0.007

Horsepower -0.0124 -0.1619

T-Value -2.01 -5.04

P-Value 0.046 0.000

HPsq 0.00040

T-Value 4.73

P-Value 0.000

S 2.50 2.43 2.23 2.17 2.14 1.96

R-Sq 66.78 68.94 74.04 75.70 76.55 80.45

R-Sq(adj) 66.50 68.40 73.36 74.85 75.51 79.41

Mallows C-p 71.5 61.4 34.8 27.4 24.7 4.8

More? (Yes, No, Subcommand, or Help)

SUBC> y

Step 7

Constant 58.50

Weight -0.00342

T-Value -5.74

P-Value 0.000

SUV_D -19.0

T-Value -2.79

P-Value 0.006

SUV_L 0.090

T-Value 2.36

P-Value 0.020

Turning Circle -0.210

T-Value -2.24

P-Value 0.027

Horsepower -0.175

T-Value -5.43

P-Value 0.000

HPsq 0.00042

T-Value 5.03

P-Value 0.000

Fuel_D 0.92

T-Value 2.11

P-Value 0.037

S 1.93

R-Sq 81.21

R-Sq(adj) 80.02

Mallows C-p 2.5

More? (Yes, No, Subcommand, or Help)

SUBC> y

No variables entered or removed

More? (Yes, No, Subcommand, or Help)

SUBC> n

MTB > Correlation 'Horsepower' 'Length' 'Width' 'Weight' 'Cargo Volume' &

CONT> 'Turning Circle' 'SUV_D' 'Fuel_D' 'SUVwt' 'SUVtc' 'HPsq' 'AWD_D' &

CONT> 'FWD_D' 'RWD_D' 'SUV_L'.

Correlations: Horsepower, Length, Width, Weight, Cargo Volume, ...

Horsepower Length Width Weight

Length 0.648

0.000

Width 0.660 0.825

0.000 0.000

Weight 0.673 0.634 0.780

0.000 0.000 0.000

Cargo Volume 0.296 0.395 0.546 0.716

0.001 0.000 0.000 0.000

Turning Circ 0.497 0.750 0.658 0.650

0.000 0.000 0.000 0.000

SUV_D 0.160 -0.102 0.180 0.535

0.080 0.265 0.049 0.000

Fuel_D 0.321 -0.013 -0.042 0.057

0.000 0.886 0.645 0.540

SUVwt 0.182 -0.077 0.206 0.562

0.045 0.403 0.023 0.000

SUVtc 0.185 -0.062 0.211 0.577

0.042 0.502 0.020 0.000

HPsq 0.989 0.632 0.645 0.668

0.000 0.000 0.000 0.000

AWD_D 0.059 -0.118 -0.037 0.065

0.523 0.199 0.691 0.483

FWD_D -0.370 -0.001 -0.163 -0.453

0.000 0.994 0.076 0.000

RWD_D 0.334 0.070 0.151 0.351

0.000 0.445 0.101 0.000

SUV_L 0.197 -0.053 0.219 0.582

0.030 0.564 0.016 0.000

Cargo Volume Turning Circ SUV_D Fuel_D

Turning Circ 0.486

0.000

SUV_D 0.459 0.139

0.000 0.127

Fuel_D -0.245 -0.069 -0.147

0.007 0.456 0.110

SUVwt 0.473 0.161 0.999 -0.141

0.000 0.078 0.000 0.125

SUVtc 0.484 0.196 0.996 -0.142

0.000 0.031 0.000 0.121

HPsq 0.289 0.480 0.173 0.296

0.001 0.000 0.058 0.001

AWD_D 0.021 -0.068 0.185 0.218

0.823 0.461 0.043 0.017

FWD_D -0.165 -0.027 -0.517 -0.280

0.071 0.771 0.000 0.002

RWD_D 0.108 0.015 0.364 0.098

0.239 0.874 0.000 0.288

SUV_L 0.487 0.181 0.996 -0.145

0.000 0.047 0.000 0.114

SUVwt SUVtc HPsq AWD_D

SUVtc 0.998

0.000

HPsq 0.198 0.200

0.030 0.028

AWD_D 0.184 0.174 0.040

0.044 0.057 0.667

FWD_D -0.522 -0.526 -0.369 -0.366

0.000 0.000 0.000 0.000

RWD_D 0.367 0.374 0.347 -0.137

0.000 0.000 0.000 0.135

SUV_L 0.999 0.998 0.215 0.176

0.000 0.000 0.018 0.054

FWD_D RWD_D

RWD_D -0.810

0.000

SUV_L -0.529 0.381

0.000 0.000

Cell Contents: Pearson correlation

P-Value

PRESS

Assesses your model's predictive ability. In general, the smaller the prediction sum of squares (PRESS) value, the better the model's predictive ability. PRESS is used to calculate the predicted R2. PRESS, similar to the error sum of squares (SSE), is the sum of squares of the prediction error. PRESS differs from SSE in that each fitted value, i, for PRESS is obtained by deleting the ith observation from the data set, estimating the regression equation from the remaining n - 1 observations, then using the fitted regression function to obtain the predicted value for the ith observation.

Predicted R2

Similar to R2. Predicted R2 indicates how well the model predicts responses for new observations, whereas R2 indicates how well the model fits your data. Predicted R2 can prevent overfitting the model and is more useful than adjusted R2 for comparing models because it is calculated with observations not included in model calculation.

Predicted R2 is between 0 and 1 and is calculated from the PRESS statistic. Larger values of predicted R2 suggest models of greater predictive ability.

MTB > Regress 'MPG' 6 'Weight' 'SUV_D' 'SUV_L' 'Turning Circle' &

CONT> 'Horsepower' 'HPsq';

SUBC> Constant;

SUBC> Brief 2.

MTB > Regress 'MPG' 6 'Weight' 'SUV_D' 'SUV_L' 'Turning Circle' &

CONT> 'Horsepower' 'HPsq';

SUBC> GNormalplot;

SUBC> NoDGraphs;

SUBC> RType 1;

SUBC> Constant;

SUBC> VIF;

SUBC> Press;

SUBC> Brief 2.

Regression Analysis: MPG versus Weight, SUV_D, ...

The regression equation is

MPG = 63.1 - 0.00303 Weight - 14.8 SUV_D + 0.0653 SUV_L - 0.264 Turning Circle

- 0.213 Horsepower + 0.000522 HPsq

Predictor Coef SE Coef T P VIF

Constant 63.105 3.978 15.86 0.000

Weight -0.0030345 0.0006859 -4.42 0.000 5.6

SUV_D -14.812 7.957 -1.86 0.065 282.1

SUV_L 0.06527 0.04478 1.46 0.148 307.9

Turning Circle -0.2639 0.1050 -2.51 0.013 2.0

Horsepower -0.21251 0.03575 -5.94 0.000 63.5

HPsq 0.00052249 0.00009459 5.52 0.000 61.3

S = 2.27485 R-Sq = 77.5% R-Sq(adj) = 76.4%

PRESS = 752.906 R-Sq(pred) = 71.34%

Analysis of Variance

Source DF SS MS F P

Regression 6 2037.34 339.56 65.62 0.000

Residual Error 114 589.95 5.17

Total 120 2627.29

Source DF Seq SS

Weight 1 1605.19

SUV_D 1 47.29

SUV_L 1 132.83

Turning Circle 1 52.31

Horsepower 1 41.83

HPsq 1 157.89

Unusual Observations

Obs Weight MPG Fit SE Fit Residual St Resid

16 5590 13.000 15.361 1.137 -2.361 -1.20 X

34 7270 10.000 6.856 1.461 3.144 1.80 X

40 5590 13.000 15.361 1.137 -2.361 -1.20 X

62 4065 19.000 14.633 0.654 4.367 2.00R

108 2150 38.000 30.489 0.632 7.511 3.44R

111 2750 41.000 33.473 1.133 7.527 3.82RX

114 2935 41.000 29.806 0.777 11.194 5.24R

115 2940 24.000 29.791 0.778 -5.791 -2.71R

R denotes an observation with a large standardized residual.

X denotes an observation whose X value gives it large influence.

MTB > Regress 'MPG' 5 'Weight' 'SUV_D' 'Turning Circle' 'Horsepower' &

CONT> 'HPsq';

SUBC> GNormalplot;

SUBC> NoDGraphs;

SUBC> RType 1;

SUBC> Constant;

SUBC> VIF;

SUBC> Press;

SUBC> Brief 2.

Regression Analysis: MPG versus Weight, SUV_D, ...

The regression equation is

MPG = 63.1 - 0.00250 Weight - 3.25 SUV_D - 0.250 Turning Circle

- 0.239 Horsepower + 0.000593 HPsq

Predictor Coef SE Coef T P VIF

Constant 63.137 3.998 15.79 0.000

Weight -0.0025020 0.0005834 -4.29 0.000 4.0

SUV_D -3.2492 0.6272 -5.18 0.000 1.7

Turning Circle -0.2501 0.1051 -2.38 0.019 1.9

Horsepower -0.23928 0.03082 -7.76 0.000 46.7

HPsq 0.00059313 0.00008163 7.27 0.000 45.2

S = 2.28595 R-Sq = 77.1% R-Sq(adj) = 76.1%

PRESS = 744.047 R-Sq(pred) = 71.68%

Analysis of Variance

Source DF SS MS F P

Regression 5 2026.35 405.27 77.56 0.000

Residual Error 115 600.94 5.23

Total 120 2627.29

Source DF Seq SS

Weight 1 1605.19

SUV_D 1 47.29

Turning Circle 1 46.32

Horsepower 1 51.65

HPsq 1 275.90

Unusual Observations

Obs Weight MPG Fit SE Fit Residual St Resid

16 5590 13.000 14.381 0.921 -1.381 -0.66 X

34 7270 10.000 5.945 1.328 4.055 2.18RX

40 5590 13.000 14.381 0.921 -1.381 -0.66 X

108 2150 38.000 30.081 0.570 7.919 3.58R

111 2750 41.000 33.910 1.098 7.090 3.54RX

114 2935 41.000 30.060 0.761 10.940 5.08R

115 2940 24.000 30.047 0.762 -6.047 -2.81R

R denotes an observation with a large standardized residual.

X denotes an observation whose X value gives it large influence.

MTB > Stepwise 'MPG' 'Horsepower' 'Length' 'Width' 'Weight' 'Cargo Volume' &

CONT> 'Turning Circle' 'SUV_D' 'Fuel_D' 'SUVwt' 'HPsq' 'AWD_D' &

CONT> 'FWD_D' 'RWD_D' 'SUV_L';

SUBC> AEnter 0.15;

SUBC> ARemove 0.15;

SUBC> Best 0;

SUBC> Constant.

Stepwise Regression: MPG versus Horsepower, Length, ...

Alpha-to-Enter: 0.15 Alpha-to-Remove: 0.15

Response is MPG on 14 predictors, with N = 119

N(cases with missing observations) = 2 N(all cases) = 121

Step 1 2 3 4 5 6

Constant 38.31 36.75 41.59 50.06 50.15 59.00

Weight -0.00491 -0.00436 -0.00578 -0.00495 -0.00424 -0.00339

T-Value -15.34 -11.87 -12.82 -9.31 -6.74 -5.61

P-Value 0.000 0.000 0.000 0.000 0.000 0.000

SUV_D -1.72 -33.71 -35.29 -35.12 -18.68

T-Value -2.84 -4.99 -5.36 -5.40 -2.71

P-Value 0.005 0.000 0.000 0.000 0.008

SUV_L 0.180 0.185 0.182 0.088

T-Value 4.75 5.04 5.01 2.26

P-Value 0.000 0.000 0.000 0.026

Turning Circle -0.285 -0.292 -0.255

T-Value -2.79 -2.90 -2.75

P-Value 0.006 0.004 0.007

Horsepower -0.0124 -0.1619

T-Value -2.01 -5.04

P-Value 0.046 0.000

HPsq 0.00040

T-Value 4.73

P-Value 0.000

S 2.50 2.43 2.23 2.17 2.14 1.96

R-Sq 66.78 68.94 74.04 75.70 76.55 80.45

R-Sq(adj) 66.50 68.40 73.36 74.85 75.51 79.41

Mallows C-p 71.5 61.4 34.8 27.4 24.7 4.8

More? (Yes, No, Subcommand, or Help)

SUBC> remove c20.

Step 7 8 9

Constant 59.15 59.00 58.50

Weight -0.00267 -0.00339 -0.00342

T-Value -5.10 -5.61 -5.74

P-Value 0.000 0.000 0.000

SUV_D -3.13 -18.68 -18.95

T-Value -5.51 -2.71 -2.79

P-Value 0.000 0.008 0.006

SUV_L 0.088 0.090

T-Value 2.26 2.36

P-Value 0.026 0.020

Turning Circle -0.236 -0.255 -0.210

T-Value -2.51 -2.75 -2.24

P-Value 0.013 0.007 0.027

Horsepower -0.199 -0.162 -0.175

T-Value -7.09 -5.04 -5.43

P-Value 0.000 0.000 0.000

HPsq 0.00050 0.00040 0.00042

T-Value 6.75 4.73 5.03

P-Value 0.000 0.000 0.000

Fuel_D 0.92

T-Value 2.11

P-Value 0.037

S 2.00 1.96 1.93

R-Sq 79.56 80.45 81.21

R-Sq(adj) 78.66 79.41 80.02

Mallows C-p 7.8 4.8 2.5

More? (Yes, No, Subcommand, or Help)

SUBC> enter c17 c18 c19.

Step 10 11 12 13

Constant 60.14 59.11 58.50 58.50

Weight -0.00355 -0.00346 -0.00344 -0.00342

T-Value -5.75 -5.72 -5.72 -5.74

P-Value 0.000 0.000 0.000 0.000

SUV_D -19.5 -19.1 -18.8 -19.0

T-Value -2.82 -2.77 -2.74 -2.79

P-Value 0.006 0.007 0.007 0.006

SUV_L 0.092 0.090 0.089 0.090

T-Value 2.37 2.32 2.30 2.36

P-Value 0.020 0.022 0.023 0.020

Turning Circle -0.207 -0.205 -0.202 -0.210

T-Value -2.10 -2.09 -2.07 -2.24

P-Value 0.038 0.039 0.041 0.027

Horsepower -0.175 -0.177 -0.176 -0.175

T-Value -5.33 -5.42 -5.41 -5.43

P-Value 0.000 0.000 0.000 0.000

HPsq 0.00042 0.00043 0.00042 0.00042

T-Value 4.98 5.04 5.02 5.03

P-Value 0.000 0.000 0.000 0.000

Fuel_D 0.73 0.80 0.87 0.92

T-Value 1.49 1.66 1.92 2.11

P-Value 0.139 0.099 0.057 0.037

AWD_D -1.1

T-Value -0.76

P-Value 0.451

FWD_D -1.36 -0.51 -0.17

T-Value -0.98 -0.62 -0.32

P-Value 0.331 0.535 0.752

RWD_D -1.23 -0.42

T-Value -0.93 -0.55

P-Value 0.353 0.586

S 1.95 1.95 1.94 1.93

R-Sq 81.37 81.27 81.22 81.21

R-Sq(adj) 79.65 79.73 79.86 80.02

Mallows C-p 7.6 6.1 4.4 2.5

More? (Yes, No, Subcommand, or Help)

SUBC> no

Results for: 252x0504-41.MTW

MTB > WSave "C:\Documents and Settings\rbove\My Documents\Minitab\252x0504-41.MTW";

SUBC> Replace.

Saving file as: 'C:\Documents and Settings\rbove\My

Documents\Minitab\252x0504-41.MTW'

MTB > erase c21

MTB > Regress 'MPG' 6 'Weight' 'SUV_D' 'SUV_L' 'Turning Circle' &

CONT> 'Horsepower' 'HPsq' ;

SUBC> GNormalplot;

SUBC> NoDGraphs;

SUBC> RType 1;

SUBC> Constant;

SUBC> VIF;

SUBC> Press;

SUBC> Brief 2.

Regression Analysis: MPG versus Weight, SUV_D, ...

The regression equation is

MPG = 64.4 - 0.00284 Weight - 15.8 SUV_D + 0.0694 SUV_L - 0.305 Turning Circle

- 0.214 Horsepower + 0.000524 HPsq

Predictor Coef SE Coef T P VIF

Constant 64.364 3.973 16.20 0.000

Weight -0.0028431 0.0006832 -4.16 0.000 5.7

SUV_D -15.843 7.867 -2.01 0.046 276.4

SUV_L 0.06943 0.04423 1.57 0.119 301.7

Turning Circle -0.3045 0.1055 -2.89 0.005 2.0

Horsepower -0.21444 0.03528 -6.08 0.000 63.1

HPsq 0.00052386 0.00009332 5.61 0.000 61.0

S = 2.24427 R-Sq = 78.3% R-Sq(adj) = 77.2%

PRESS = 725.963 R-Sq(pred) = 72.34%

Analysis of Variance

Source DF SS MS F P

Regression 6 2055.21 342.54 68.01 0.000

Residual Error 113 569.15 5.04

Total 119 2624.37

Source DF Seq SS

Weight 1 1602.61

SUV_D 1 49.58

SUV_L 1 135.39

Turning Circle 1 61.04

Horsepower 1 47.88

HPsq 1 158.71

Unusual Observations

Obs Weight MPG Fit SE Fit Residual St Resid

16 5590 13.000 15.259 1.123 -2.259 -1.16 X

34 7270 10.000 6.907 1.442 3.093 1.80 X

36 2715 24.000 28.432 0.493 -4.432 -2.02R

40 5590 13.000 15.259 1.123 -2.259 -1.16 X

107 2150 38.000 30.543 0.624 7.457 3.46R

110 2750 41.000 33.747 1.126 7.253 3.74RX

113 2935 41.000 30.000 0.772 11.000 5.22R

114 2940 24.000 29.985 0.774 -5.985 -2.84R

R denotes an observation with a large standardized residual.

X denotes an observation whose X value gives it large influence.

MTB > Regress 'MPG' 5 'Weight' 'SUV_D' 'Turning Circle' 'Horsepower' &

CONT> 'HPsq' ;

SUBC> GNormalplot;

SUBC> NoDGraphs;

SUBC> RType 1;

SUBC> Constant;

SUBC> VIF;

SUBC> Press;

SUBC> Brief 2.

Regression Analysis: MPG versus Weight, SUV_D, ...

The regression equation is

MPG = 64.4 - 0.00228 Weight - 3.53 SUV_D - 0.288 Turning Circle

- 0.243 Horsepower + 0.000599 HPsq

Predictor Coef SE Coef T P VIF

Constant 64.352 3.999 16.09 0.000

Weight -0.0022848 0.0005871 -3.89 0.000 4.2

SUV_D -3.5330 0.6366 -5.55 0.000 1.8

Turning Circle -0.2884 0.1057 -2.73 0.007 2.0

Horsepower -0.24278 0.03051 -7.96 0.000 46.6

HPsq 0.00059879 0.00008071 7.42 0.000 45.0

S = 2.25865 R-Sq = 77.8% R-Sq(adj) = 76.9%

PRESS = 720.507 R-Sq(pred) = 72.55%

Analysis of Variance

Source DF SS MS F P

Regression 5 2042.80 408.56 80.09 0.000

Residual Error 114 581.57 5.10

Total 119 2624.37

Source DF Seq SS

Weight 1 1602.61

SUV_D 1 49.58

Turning Circle 1 52.45

Horsepower 1 57.33

HPsq 1 280.82

Unusual Observations

Obs Weight MPG Fit SE Fit Residual St Resid

16 5590 13.000 14.223 0.914 -1.223 -0.59 X

34 7270 10.000 5.938 1.312 4.062 2.21RX

40 5590 13.000 14.223 0.914 -1.223 -0.59 X

107 2150 38.000 30.108 0.563 7.892 3.61R

110 2750 41.000 34.201 1.095 6.799 3.44RX

113 2935 41.000 30.262 0.759 10.738 5.05R

114 2940 24.000 30.251 0.760 -6.251 -2.94R

R denotes an observation with a large standardized residual.

X denotes an observation whose X value gives it large influence.

MTB > Regress 'MPG' 8 'Weight' 'SUV_D' 'Turning Circle' 'Horsepower' &

CONT> 'HPsq' 'AWD_D' 'FWD_D' 'RWD_D';

SUBC> GNormalplot;

SUBC> NoDGraphs;

SUBC> RType 1;

SUBC> Constant;

SUBC> VIF;

SUBC> Press;

SUBC> Brief 2.

Regression Analysis: MPG versus Weight, SUV_D, ...

The regression equation is

MPG = 66.4 - 0.00248 Weight - 3.83 SUV_D - 0.254 Turning Circle

- 0.251 Horsepower + 0.000618 HPsq - 1.21 AWD_D - 2.10 FWD_D - 1.70 RWD_D

Predictor Coef SE Coef T P VIF

Constant 66.435 4.400 15.10 0.000

Weight -0.0024795 0.0006077 -4.08 0.000 4.4

SUV_D -3.8302 0.6814 -5.62 0.000 2.0

Turning Circle -0.2541 0.1116 -2.28 0.025 2.2

Horsepower -0.25082 0.03122 -8.03 0.000 48.6

HPsq 0.00061833 0.00008244 7.50 0.000 46.7

AWD_D -1.213 1.620 -0.75 0.455 3.4

FWD_D -2.103 1.490 -1.41 0.161 11.2

RWD_D -1.697 1.434 -1.18 0.239 8.6

S = 2.26416 R-Sq = 78.3% R-Sq(adj) = 76.8%

PRESS = 727.840 R-Sq(pred) = 72.27%

Analysis of Variance

Source DF SS MS F P

Regression 8 2055.33 256.92 50.12 0.000

Residual Error 111 569.03 5.13

Total 119 2624.37

Source DF Seq SS

Weight 1 1602.61

SUV_D 1 49.58

Turning Circle 1 52.45

Horsepower 1 57.33

HPsq 1 280.82

AWD_D 1 2.00

FWD_D 1 3.36

RWD_D 1 7.17

Unusual Observations

Obs Weight MPG Fit SE Fit Residual St Resid

34 7270 10.000 5.609 1.377 4.391 2.44RX

57 4735 14.000 13.622 1.447 0.378 0.22 X

72 4720 15.000 15.901 1.374 -0.901 -0.50 X

107 2150 38.000 30.231 0.574 7.769 3.55R

109 5435 14.000 13.477 1.338 0.523 0.29 X

110 2750 41.000 34.346 1.106 6.654 3.37RX

113 2935 41.000 30.341 0.765 10.659 5.00R

114 2940 24.000 30.329 0.766 -6.329 -2.97R

R denotes an observation with a large standardized residual.

X denotes an observation whose X value gives it large influence.

Part II

1. Time series problem.

————— 4/28/2005 6:18:32 PM ————————————————————

Welcome to Minitab, press F1 for help.

MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\252x0504-5.MTW".

Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My

Documents\Minitab\252x0504-5.MTW'

Worksheet was saved on Fri Apr 29 2005

Results for: 252x0504-5.MTW

MTB > let c3=c2*c2

MTB > Save "C:\Documents and Settings\rbove\My Documents\Minitab\252x0504-5.MTW";

SUBC> Replace.

Saving file as: 'C:\Documents and Settings\rbove\My

Documents\Minitab\252x0504-5.MTW'

Existing file replaced.

MTB > Execute "C:\Documents and Settings\rbove\My Documents\Minitab\252OLS2.mtb" 1.

Executing from file: C:\Documents and Settings\rbove\My Documents\Minitab\252OLS2.mtb

Regression Analysis: Y versus T

The regression equation is

Y = 56.7 + 1.54 T

Predictor Coef SE Coef T P

Constant 56.659 1.283 44.15 0.000

T 1.5377 0.1411 10.89 0.000

S = 2.36169 R-Sq = 90.1% R-Sq(adj) = 89.4%

Analysis of Variance

Source DF SS MS F P

Regression 1 662.05 662.05 118.70 0.000

Residual Error 13 72.51 5.58

Total 14 734.56

Unusual Observations

Obs T Y Fit SE Fit Residual St Resid

1 1.0 53.430 58.196 1.161 -4.766 -2.32R

R denotes an observation with a large standardized residual.

Regression Analysis: Y versus T, TSQ

The regression equation is

Y = 52.4 + 3.04 T - 0.0939 TSQ

Predictor Coef SE Coef T P

Constant 52.401 1.545 33.91 0.000

T 3.0405 0.4444 6.84 0.000

TSQ -0.09392 0.02701 -3.48 0.005

S = 1.73483 R-Sq = 95.1% R-Sq(adj) = 94.3%

Analysis of Variance

Source DF SS MS F P

Regression 2 698.44 349.22 116.03 0.000

Residual Error 12 36.12 3.01

Total 14 734.56

Source DF Seq SS

T 1 662.05

TSQ 1 36.39

Unusual Observations

Obs T Y Fit SE Fit Residual St Resid

5 5.0 68.650 65.255 0.605 3.395 2.09R

R denotes an observation with a large standardized residual.

Executing from file: 252OLS2namer.MTB

Executing from file: 252OLS2sumer.MTB

Data Display

Row Y T TSQ C4 x1sq

1 53.43 1 1 1

2 59.09 2 4 4

3 59.58 3 9 9

4 64.75 4 16 16

5 68.65 5 25 25

6 65.53 6 36 36

7 68.44 7 49 49

8 70.93 8 64 64

9 72.85 9 81 81

10 73.60 10 100 100

11 72.93 11 121 121

12 75.14 12 144 144

13 73.88 13 169 169

14 76.55 14 196 196

15 79.05 15 225 225

* NOTE * One or more variables are undefined.

Data Display

Row x2sq ysq x1y x2y x1x2

1 1 2854.76 53.43 53.4 1

2 16 3491.63 118.18 236.4 8

3 81 3549.78 178.74 536.2 27

4 256 4192.56 259.00 1036.0 64

5 625 4712.82 343.25 1716.3 125

6 1296 4294.18 393.18 2359.1 216

7 2401 4684.03 479.08 3353.6 343

8 4096 5031.06 567.44 4539.5 512

9 6561 5307.12 655.65 5900.9 729

10 10000 5416.96 736.00 7360.0 1000

11 14641 5318.78 802.23 8824.5 1331

12 20736 5646.02 901.68 10820.2 1728

13 28561 5458.25 960.44 12485.7 2197

14 38416 5859.90 1071.70 15003.8 2744

15 50625 6248.90 1185.75 17786.3 3375

Data Display

sumy 1034.40

sumx1 120.000

sumx2 1240.00

n 15.0000

smx1sq 1240.00

smx2sq 178312

smysq 72066.8

smx1y 8705.75

smx2y 92011.7

smx1x2 14400.0

Executing from file: 252OLS2mean.MTB

Data Display

ybar 68.9600

x1bar 8.00000

x2bar 82.6667

Executing from file: 252OLS2ss.MTB

Data Display

SSx1 280.000

SSx2 75805.3

SSy 734.556

Sx1y 430.550

Sx2y 6501.33

Sx1x2 4480.00

MTB > print c1-c3

Data Display

Row Y T TSQ

1 53.43 1 1

2 59.09 2 4

3 59.58 3 9

4 64.75 4 16

5 68.65 5 25

6 65.53 6 36

7 68.44 7 49

8 70.93 8 64

9 72.85 9 81

10 73.60 10 100

11 72.93 11 121

12 75.14 12 144

13 73.88 13 169

14 76.55 14 196

15 79.05 15 225

MTB >

Problem 4 - ANOVA etc

————— 4/28/2005 6:18:32 PM ————————————————————

Welcome to Minitab, press F1 for help.

MTB > Stack 'x1' 'x2' 'x3' 'x4' c10;

SUBC> Subscripts c11;

SUBC> UseNames.

MTB > Rank c10 c12.

MTB > Unstack (c12);

SUBC> Subscripts c11;

SUBC> After;

SUBC> VarNames.

MTB > print c1-c5

Data Display

Row Student x1 x2 x3 x4

1 Loopy 8.75 9.5 8.5 11.5

2 Percival 9.50 4.0 8.5 11.0

3 Poopsy 9.25 5.5 7.5 7.5

4 Dizzy 9.50 8.5 7.5 7.5

5 Booger 9.25 4.5 8.0 8.0

MTB > print c1 c2 c6 c3 c7 c4 c8 c5 c9

Data Display

Row Student x1 r1 x2 r2 x3 r3 x4 r4

1 Loopy 8.75 13.0 9.5 17 8.5 11.0 11.5 20.0

2 Percival 9.50 17.0 4.0 1 8.5 11.0 11.0 19.0

3 Poopsy 9.25 14.5 5.5 3 7.5 5.5 7.5 5.5

4 Dizzy 9.50 17.0 8.5 11 7.5 5.5 7.5 5.5

5 Booger 9.25 14.5 4.5 2 8.0 8.5 8.0 8.5

MTB > let c13 = c2+c3+c4+c5

MTB > let c14 = (c2*c2) + (c3*c3) + (c4*c4) + (c5*c5)

MTB > sum c2

Sum of x1

Sum of x1 = 46.25

MTB > ssq c2

Sum of Squares of x1

Sum of squares (uncorrected) of x1 = 428.188

MTB > sum c3

Sum of x2

Sum of x2 = 32

MTB > ssq c3

Sum of Squares of x2

Sum of squares (uncorrected) of x2 = 229

MTB > sum c4

Sum of x3

Sum of x3 = 40

MTB > ssq c4

Sum of Squares of x3

Sum of squares (uncorrected) of x3 = 321

MTB > sum c5

Sum of x4

Sum of x4 = 45.5

MTB > ssq c5

Sum of Squares of x4

Sum of squares (uncorrected) of x4 = 429.75

MTB > print c13 c14

Data Display

Row C13 C14

1 38.25 371.313

2 33.00 299.500

3 29.75 228.313

4 33.00 275.000

5 29.75 233.813

Results for: 252x0504-6.MTW

MTB > WSave "C:\Documents and Settings\rbove\My Documents\Minitab\252x0504-6.MTW";

SUBC> Replace.

Saving file as: 'C:\Documents and Settings\rbove\My

Documents\Minitab\252x0504-6.MTW'

MTB >

————— 5/5/2005 6:38:07 PM ————————————————————

Welcome to Minitab, press F1 for help.

MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\252x0504-6a.MTW".

Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My

Documents\Minitab\252x0504-6a.MTW'

Worksheet was saved on Thu May 05 2005

Results for: 252x0504-6a.MTW

MTB > print c1-c4

Data Display

Row C1 C2 C3 C4

1 8.75 9.5 8.5 11.5

2 9.50 4.0 8.5 11.0

3 9.25 5.5 7.5 7.5

4 9.50 8.5 7.5 7.5

5 9.25 4.5 8.0 8.0

MTB > exec '2522way4'

Executing from file: 2522way4.MTB

Executing from file: 2522onw4.MTB

One-way ANOVA: C1, C2, C3, C4

Source DF SS MS F P

Factor 3 25.96 8.65 3.35 0.045

Error 16 41.28 2.58

Total 19 67.23

S = 1.606 R-Sq = 38.61% R-Sq(adj) = 27.10%

Individual 95% CIs For Mean Based on

Pooled StDev

Level N Mean StDev ------+------+------+------+--

C1 5 9.250 0.306 (------*------)

C2 5 6.400 2.460 (------*------)

C3 5 8.000 0.500 (------*------)

C4 5 9.100 1.981 (------*------)

------+------+------+------+--

6.0 7.5 9.0 10.5

Pooled StDev = 1.606

Executing from file: 2522onme4.MTB

Executing from file: 2522osme4.MTB

Data Display

Row C1 C2 C3 C4

1 8.75 9.5 8.5 11.5

2 9.50 4.0 8.5 11.0

3 9.25 5.5 7.5 7.5

4 9.50 8.5 7.5 7.5

5 9.25 4.5 8.0 8.0

Data Display

Row x1sq x2sq x3sq x4sq

1 76.5625 90.25 72.25 132.25

2 90.2500 16.00 72.25 121.00

3 85.5625 30.25 56.25 56.25

4 90.2500 72.25 56.25 56.25

5 85.5625 20.25 64.00 64.00

Data Display

sumx1 46.2500

sumx2 32.0000

sumx3 40.0000

sumx4 45.5000

n1 5.00000

n2 5.00000

n3 5.00000

n4 5.00000

smx1sq 428.188

smx2sq 229.000

smx3sq 321.000

smx4sq 429.750

Executing from file: 2522omea4.MTB

Data Display

x1bar 9.25000

x2bar 6.40000

x3bar 8.00000

x4bar 9.10000

Data Display

smxsq 1407.94

n 20.0000

sumx 163.750

srss 1407.94

gdmn 8.18750

srmsq 338.199

x1bsq 85.5625

x2bsq 40.9600

x3bsq 64.0000

x4bsq 82.8100

sxbsq 273.333

K26 1340.70

SSR 12.0938

SSC 25.9594

SST 67.2344

Data Display

Row C1 C2 C3 C4 rsum rmn rss rmnsq

1 8.75 9.5 8.5 11.5 38.25 9.5625 371.313 91.4414

2 9.50 4.0 8.5 11.0 33.00 8.2500 299.500 68.0625

3 9.25 5.5 7.5 7.5 29.75 7.4375 228.313 55.3164

4 9.50 8.5 7.5 7.5 33.00 8.2500 275.000 68.0625

5 9.25 4.5 8.0 8.0 29.75 7.4375 233.813 55.3164

Executing from file: 2522wr1.MTB

Executing from file: 252-2W1O.MTB

Tabulated statistics: C41, C42

Rows: C41 Columns: C42

1 2 3 4 All

1 1 1 1 1 4

2 1 1 1 1 4

3 1 1 1 1 4

4 1 1 1 1 4

5 1 1 1 1 4

All 5 5 5 5 20

Cell Contents: Count

Tabulated statistics: C41, C42

Rows: C41 Columns: C42

1 2 3 4

1 8.75 9.50 8.50 11.50

2 9.50 4.00 8.50 11.00

3 9.25 5.50 7.50 7.50

4 9.50 8.50 7.50 7.50

5 9.25 4.50 8.00 8.00

Cell Contents: C40 : DATA

Tabulated statistics: C41, C42

Rows: C41 Columns: C42

1 2 3 4 All

1 8.750 9.500 8.500 11.500 9.563

2 9.500 4.000 8.500 11.000 8.250

3 9.250 5.500 7.500 7.500 7.438

4 9.500 8.500 7.500 7.500 8.250

5 9.250 4.500 8.000 8.000 7.438

All 9.250 6.400 8.000 9.100 8.188

Cell Contents: C40 : Mean

Two-way ANOVA: C40 versus C41, C42

Source DF SS MS F P

C41 4 12.0938 3.02344 1.24 0.344

C42 3 25.9594 8.65312 3.56 0.048

Error 12 29.1813 2.43177

Total 19 67.2344

S = 1.559 R-Sq = 56.60% R-Sq(adj) = 31.28%

Executing from file: 2522wfo4.MTB

Data Display

Row C31 C32 C33 C38 C34 C35 C36 C37

1 8.750 9.50 8.5 11.50 38.25 9.5625 371.31 91.441

2 9.500 4.00 8.5 11.00 33.00 8.2500 299.50 68.063

3 9.250 5.50 7.5 7.50 29.75 7.4375 228.31 55.316

4 9.500 8.50 7.5 7.50 33.00 8.2500 275.00 68.063

5 9.250 4.50 8.0 8.00 29.75 7.4375 233.81 55.316

6 46.250 32.00 40.0 45.50 163.75 8.1875 1407.94 338.199

7 5.000 5.00 5.0 5.00 20.00

8 9.250 6.40 8.0 9.10 8.19

9 428.188 229.00 321.0 429.75 1407.94

10 85.563 40.96 64.0 82.81 273.33

Data Display

Row SS. DF. MS. F.

1 12.0938 4 3.02344 1.24331

2 25.9594 3 8.65312 3.55836

3 29.1813 12 2.43177 1.00000

4 67.2344 19 3.53865 1.45517

MTB >

Problem 5 - Chisquared

Effectiveness / D u r a / t i o n
< 1 mo. / 1-2 mo. / 2-4 mo. / >4 mo. / Total
Very Effective / 15 / 28 / 24 / 6 / 73
Effective / 9 / 26 / 33 / 19 / 87
Ineffective / 5 / 2 / 3 / 5 / 15
Total / 29 / 56 / 60 / 30 / 175

————— 5/5/2005 10:42:53 PM ————————————————————

Welcome to Minitab, press F1 for help.

MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\252x0504-7.MTW".

Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My

Documents\Minitab\252x0504-7.MTW'

Worksheet was saved on Fri Apr 29 2005

Results for: 252x0504-8.MTW

MTB > WSave "C:\Documents and Settings\rbove\My Documents\Minitab\252x0504-8.MTW";

SUBC> Replace.

Saving file as: 'C:\Documents and Settings\rbove\My

Documents\Minitab\252x0504-8.MTW'

MTB > let c14 = c10 + c11 + c12 +c13

MTB > sum c14

Sum of totO

Sum of totO = 175

MTB > let c15=c14/175

MTB > let k10= sum (c10)

MTB > let c20 = c15* k10

MTB > let k11 = sum (c11)

MTB > let c21 = c15* k11

MTB > let k12 = sum (c12)

MTB > let c22 = k12 * c15

MTB > let k13 = sum (c13)

MTB > let c23 = k13 * c15

MTB > let c24 = c20 + c21 + c22 + c23

MTB > let k20 = sum c20

MTB > let k20 = sum(c20)

MTB > let k21 = sum(c21)

MTB > let k22 = sum (c22)

MTB > let k23 = sum (c23)

MTB > print k10 k21 k11 k21 k12 k22 k13 k23

Data Display

K10 29.0000

K20 29.0000

K11 56.0000

K21 56.0000

K12 60.0000

K22 60.0000

K13 30.0000

K23 30.0000

MTB > let c30 = c20

MTB > let c31 = c21

MTB > let c30 = 100 * c20

MTB > let c31 = 100 * c21

MTB > let c32 = 100 * c22

MTB > let c33 = 100 * c23

MTB > round c30 c30

MTB > round c31 c31

MTB > round c32 c32

MTB > round c33 c33

MTB > let c30 = c30/100

MTB > let c31 = c31/100

MTB > let c32 = c32/100

MTB > let c33 = c33/100

MTB > let c34 = c30 + c31+ c32 + c33

MTB > sum c30

Sum of 1moE1

Sum of 1moE1 = 29.01

MTB > sum c31

Sum of 2moE1

Sum of 2moE1 = 56

MTB > sum c32

Sum of 4moE1

Sum of 4moE1 = 60

MTB > sum c33

Sum of momoE1

Sum of momoE1 = 29.99

MTB > print c10 - c14

Data Display

Row 1mo 2mo 4mo momo totO

1 15 28 24 6 73

2 9 26 33 19 87

3 5 2 3 5 15

MTB > print c10 - c15

Data Display

Row 1mo 2mo 4mo momo totO pr

1 15 28 24 6 73 0.417143

2 9 26 33 19 87 0.497143

3 5 2 3 5 15 0.085714

MTB > print c20 - c24

Data Display

Row 1moE 2moE 4moE momoE totE

1 12.0971 23.36 25.0286 12.5143 73

2 14.4171 27.84 29.8286 14.9143 87

3 2.4857 4.80 5.1429 2.5714 15

MTB > print c30 - c34

Data Display

Row 1moE1 2moE1 4moE1 momoE1 C34

1 12.10 23.36 25.03 12.51 73

2 14.42 27.84 29.83 14.91 87

3 2.49 4.80 5.14 2.57 15

MTB > Stack c10 c11 c12 c13 c1.

MTB > stack c30 c31 c32 c33 c2.

MTB > sum c1

Sum of C1

Sum of C1 = 175

MTB > sum c2

Sum of C2

Sum of C2 = 175

MTB > exec '252chisq'

Executing from file: 252chisq.MTB

Data Display

Row O E C3 C4 C5 C6

1 15 12.10 -2.90 8.4100 0.69504 18.5950

2 9 14.42 5.42 29.3764 2.03720 5.6172

3 5 2.49 -2.51 6.3001 2.53016 10.0402

4 28 23.36 -4.64 21.5296 0.92164 33.5616

5 26 27.84 1.84 3.3856 0.12161 24.2816

6 2 4.80 2.80 7.8400 1.63333 0.8333

7 24 25.03 1.03 1.0609 0.04239 23.0124

8 33 29.83 -3.17 10.0489 0.33687 36.5069

9 3 5.14 2.14 4.5796 0.89097 1.7510

10 6 12.51 6.51 42.3801 3.38770 2.8777

11 19 14.91 -4.09 16.7281 1.12194 24.2119

12 5 2.57 -2.43 5.9049 2.29763 9.7276

Data Display

n 175.000

K2 175.000

K3 -0.000000000

chisq1 16.0165

chisq 16.0165

K6 191.016

MTB > print c1-c6

Data Display

Row O E O-E O-Esq O-esq/E Osq/E

1 15 12.10 -2.90 8.4100 0.69504 18.5950

2 9 14.42 5.42 29.3764 2.03720 5.6172

3 5 2.49 -2.51 6.3001 2.53016 10.0402

4 28 23.36 -4.64 21.5296 0.92164 33.5616

5 26 27.84 1.84 3.3856 0.12161 24.2816

6 2 4.80 2.80 7.8400 1.63333 0.8333

7 24 25.03 1.03 1.0609 0.04239 23.0124

8 33 29.83 -3.17 10.0489 0.33687 36.5069

9 3 5.14 2.14 4.5796 0.89097 1.7510

10 6 12.51 6.51 42.3801 3.38770 2.8777

11 19 14.91 -4.09 16.7281 1.12194 24.2119

12 5 2.57 -2.43 5.9049 2.29763 9.7276

MTB > Save "C:\Documents and Settings\rbove\My Documents\Minitab\252x0504-8.MTW";

SUBC> Replace.

Saving file as: 'C:\Documents and Settings\rbove\My

Documents\Minitab\252x0504-8.MTW'

Existing file replaced.

Problem 5 - 2 proportions.

————— 5/6/2005 1:14:09 AM ————————————————————

Welcome to Minitab, press F1 for help.

Results for: 252x0504-8a.MTW

MTB > erase k1 -k200

MTB > erase c1-c100

MTB > exec '252-2p1'

Executing from file: 252-2p1.MTB

Executing from file: 252-2prp.MTB

Data Display

x1 7.00000

n1 65.0000

p1 0.107692

x2 8.00000

n2 90.0000

p2 0.0888889

Data Display

p0 0.0967742

n 155.000

sdp2 0.0487672

q0 0.903226

q1 0.892308

q2 0.911111

K213 0.00147838

K214 0.000899863

K215 0.00231596

sdp1 0.0481245

K217 0.0188034

K218 0.00237824

Data Display

1 poold 0

delp 0.0188034

MTB > Save "C:\Documents and Settings\rbove\My Documents\Minitab\252x0504-8a.MTW";

SUBC> Replace.

Saving file as: 'C:\Documents and Settings\rbove\My

Documents\Minitab\252x0504-8a.MTW'

Existing file replaced.

MTB >

Problem 5 - Poisson problem

e) (Anderson et. al.) The number of emergency calls our Fire department receives is believed to have a Poisson distribution with a parameter of 3. Test this against data for a period of 120 days: 0 calls on 9 days, 1 call on 12 days, 2 calls on 30 days, 3 calls on 27 days, 4 calls on 22 days. 5 calls on 13 days and 7 calls on 6 days. (5)

This is the Poisson 3 table.

252y0541s 5/7/05

k P(x=k) P(xk)

0 0.049787 0.04979

1 0.149361 0.19915

2 0.224042 0.42319

3 0.224042 0.64723

4 0.168031 0.81526

5 0.100819 0.91608

6 0.050409 0.96649

7 0.021604 0.98810

8 0.008102 0.99620

9 0.002701 0.99890

10 0.000810 0.99971

11 0.000221 0.99993

12 0.000055 0.99998

13 0.000013 1.00000

14 0.000003 1.00000

15 0.000001 1.00000

16 0.000000 1.00000

17 0.000000 1.00000

P(x=k)

0.049787

0.149361

0.224042

0.168031

0.100819

0.050409

0.021604

0.008102

0.002701

0.000810

0.000221

0.000055

0.000013

0.000003

0.000001

0.000000

P(xk)

0.04979

0.19915

0.42319

0.64723

0.81526

0.91608

0.96649

0.98810

0.99620

0.99890

0.99971

0.99993

0.99998

1.00000

252y0541s 5/7/05

————— 5/6/2005 1:14:09 AM ————————————————————

Welcome to Minitab, press F1 for help.

MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\252x0504-8b.MTW".

Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My

Documents\Minitab\252x0504-8b.MTW'

Worksheet was saved on Fri May 06 2005

Results for: 252x0504-8b1.MTW

MTB > WSave "C:\Documents and Settings\rbove\My Documents\Minitab\252x0504-8b1.MTW";

SUBC> Replace.

Saving file as: 'C:\Documents and Settings\rbove\My

Documents\Minitab\252x0504-8b1.MTW'

MTB > let c1 = c10

MTB > let c2 = c11

MTB > exec '252chisq'

Executing from file: 252chisq.MTB

Data Display

Row O E C3 C4 C5 C6

1 9 5.9744 -3.02556 9.1540 1.53220 13.5578

2 12 17.9233 5.92332 35.0857 1.95755 8.0342

3 30 26.8850 -3.11496 9.7030 0.36091 33.4759

4 27 26.8850 -0.11496 0.0132 0.00049 27.1155

5 22 20.1637 -1.83628 3.3719 0.16723 24.0035

6 13 12.0983 -0.90172 0.8131 0.06721 13.9689

7 7 10.0704 3.07040 9.4274 0.93615 4.8657

Data Display

n 120.000

K2 120.000

K3 0.000240000

chisq1 5.02148

chisq 5.02172

K6 125.021

MTB > print c10-c14

Data Display

Row O1 E2 f E1 Fcum

1 9 5.9744 0.049787 5.9744 0.04979

2 12 17.9233 0.149361 17.9233 0.19915

3 30 26.8850 0.224042 26.8850 0.42319

4 27 26.8850 0.224042 26.8850 0.64723

5 22 20.1637 0.168031 20.1637 0.81526

6 13 12.0983 0.100819 12.0983 0.91608

7 7 10.0704 0.050409 6.0491 0.96649

8 0.021604 2.5925 0.98810

9 0.008102 0.9722 0.99620

10 0.002701 0.3241 0.99890

11 0.000810 0.0972 0.99971

12 0.000221 0.0265 0.99993

13 0.000055 0.0066 0.99998

14 0.000013 0.0016 1.00000

15 0.000003 0.0004 1.00000

16 0.000001 0.0001 1.00000

17 0.000000 0.0000 1.00000

18 0.000000 0.0000 1.00000

————— 5/6/2005 1:14:07 AM ————————————————————

Welcome to Minitab, press F1 for help.

MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\252x0504-8b2.MTW".

Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My

Documents\Minitab\252x0504-8b2.MTW'

Worksheet was saved on Fri May 06 2005

Results for: 252x0504-8b2.MTW

MTB > exec '252KSO'

Executing from file: 252KSO.MTB

Executing from file: 252ksc.MTB

Data Display

Row O O/n FO

1 9 0.075000 0.07500

2 12 0.100000 0.17500

3 30 0.250000 0.42500

4 27 0.225000 0.65000

5 22 0.183333 0.83333

6 13 0.108333 0.94167

7 7 0.058333 1.00000

Data Display

n 120.000

MTB > exec '252ks'

Executing from file: 252ks.MTB

Data Display

Row FE D

1 0.04979 0.0252100

2 0.19915 0.0241500

3 0.42319 0.0018100

4 0.64723 0.0027700

5 0.81526 0.0180733

6 0.91608 0.0255867

7 0.96649 0.0335100

8 0.98810 0.0119000

9 0.99620 0.0038000

10 0.99890 0.0011000

11 0.99971 0.0002900

12 0.99993 0.0000700

13 0.99998 0.0000200

14 1.00000 0.0000000

15 1.00000 0.0000000

16 1.00000 0.0000000

17 1.00000 0.0000000

18 1.00000 0.0000000

Data Display

max D 0.0335100

MTB > print c1 c6 c3 c4 c5

Data Display

Row O O/n FO FE D

1 9 0.075000 0.07500 0.04979 0.0252100

2 12 0.100000 0.17500 0.19915 0.0241500

3 30 0.250000 0.42500 0.42319 0.0018100

4 27 0.225000 0.65000 0.64723 0.0027700

5 22 0.183333 0.83333 0.81526 0.0180733

6 13 0.108333 0.94167 0.91608 0.0255867

7 7 0.058333 1.00000 0.96649 0.0335100

8 1.00000 0.98810 0.0119000

9 1.00000 0.99620 0.0038000

10 1.00000 0.99890 0.0011000

11 1.00000 0.99971 0.0002900

12 1.00000 0.99993 0.0000700

13 1.00000 0.99998 0.0000200

14 1.00000 1.00000 0.0000000

15 1.00000 1.00000 0.0000000

16 1.00000 1.00000 0.0000000

17 1.00000 1.00000 0.0000000

18 1.00000 1.00000 0.0000000

MTB >

Problem 6

————— 4/29/2005 4:38:10 AM ————————————————————

Welcome to Minitab, press F1 for help.

Results for: 252x0504-7.MTW

MTB > WSave "C:\Documents and Settings\rbove\My Documents\Minitab\252x0504-7.MTW";

SUBC> Replace.

Saving file as: 'C:\Documents and Settings\rbove\My

Documents\Minitab\252x0504-7.MTW'

MTB > let d = c2-c3

MTB > sum c2

Sum of 2001

Sum of 2001 = 2860.46

MTB > ssq c2

Sum of Squares of 2001

Sum of squares (uncorrected) of 2001 = 953941

MTB > sum c3

Sum of 2002

Sum of 2002 = 2954.56

MTB > ssq c3

Sum of Squares of 2002

Sum of squares (uncorrected) of 2002 = 999629

MTB > sum c4

Sum of d

Sum of d = -94.104

MTB > ssq c4

Sum of Squares of d

Sum of squares (uncorrected) of d = 3724.97

MTB > print c1-c4

Data Display

Row Location 2001 2002 d

1 Alexandria 245.795 293.266 -47.471

2 Boston 391.750 408.803 -17.053

3 Decatur 205.270 227.561 -22.291

4 Kirkland 326.524 333.569 -7.045

5 New York 545.363 531.098 14.265

6 Philadephia 185.736 197.874 -12.138

7 Phoenix 170.413 175.030 -4.617

8 Raleigh 210.015 196.094 13.921

9 San Bruno 385.387 391.409 -6.022

10 Tampa 194.205 199.858 -5.653

MTB > Save "C:\Documents and Settings\rbove\My Documents\Minitab\252x0504-7.MTW";

SUBC> Replace.

Saving file as: 'C:\Documents and Settings\rbove\My

Documents\Minitab\252x0504-7.MTW'

Existing file replaced.

MTB >

————— 5/6/2005 6:05:38 AM ————————————————————

Welcome to Minitab, press F1 for help.

MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\252x0504-7.MTW".

Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My

Documents\Minitab\252x0504-7.MTW'

Worksheet was saved on Fri Apr 29 2005

Results for: 252x0504-7.MTW

MTB > Rank 'd' c5.

MTB > print c1-c5

Data Display

Row Location 2001 2002 d C5

1 Alexandria 245.795 293.266 -47.471 1

2 Boston 391.750 408.803 -17.053 3

3 Decatur 205.270 227.561 -22.291 2

4 Kirkland 326.524 333.569 -7.045 5

5 New York 545.363 531.098 14.265 10

6 Philadephia 185.736 197.874 -12.138 4

7 Phoenix 170.413 175.030 -4.617 8

8 Raleigh 210.015 196.094 13.921 9

9 San Bruno 385.387 391.409 -6.022 6

10 Tampa 194.205 199.858 -5.653 7

MTB > let c6 = c4

MTB > let c5 = absolute(c4)

MTB > rank c5 c6

MTB > print c1-c6

Data Display

Row Location 2001 2002 d C5 C6

1 Alexandria 245.795 293.266 -47.471 47.471 10

2 Boston 391.750 408.803 -17.053 17.053 8

3 Decatur 205.270 227.561 -22.291 22.291 9

4 Kirkland 326.524 333.569 -7.045 7.045 4

5 New York 545.363 531.098 14.265 14.265 7

6 Philadephia 185.736 197.874 -12.138 12.138 5

7 Phoenix 170.413 175.030 -4.617 4.617 1

8 Raleigh 210.015 196.094 13.921 13.921 6

9 San Bruno 385.387 391.409 -6.022 6.022 3

10 Tampa 194.205 199.858 -5.653 5.653 2

MTB > Stack c2 c3 c10;

SUBC> Subscripts c11;

SUBC> UseNames.

MTB > Rank c10 c12.

MTB > Unstack (c12);

SUBC> Subscripts c11;

SUBC> After;

SUBC> VarNames.

MTB > print c1 c2 c13 c3 c14

Data Display

Row Location 2001 C12_2001 2002 C12_2002

1 Alexandria 245.795 11 293.266 12

2 Boston 391.750 17 408.803 18

3 Decatur 205.270 8 227.561 10

4 Kirkland 326.524 13 333.569 14

5 New York 545.363 20 531.098 19

6 Philadephia 185.736 3 197.874 6

7 Phoenix 170.413 1 175.030 2

8 Raleigh 210.015 9 196.094 5

9 San Bruno 385.387 15 391.409 16

10 Tampa 194.205 4 199.858 7

MTB > Save "C:\Documents and Settings\rbove\My Documents\Minitab\252x0504-7.MTW";

SUBC> Replace.

Saving file as: 'C:\Documents and Settings\rbove\My

Documents\Minitab\252x0504-7.MTW'

Existing file replaced.

MTB >

Part III

252x0541 4/22/05 ECO252 QBA2

Final EXAM

May 2-6, 2004

TAKE HOME SECTION

Name: ______

Student Number: ______

Class days and time : ______

Please Note: computer problems 2,3 and 4 should be turned in with the exam (2). In problem 2, the 2 way ANOVA table should be checked. The three F tests should be done with a 5% significance level and you should note whether there was (i) a significant difference between drivers, (ii) a significant difference between cars and (iii) significant interaction. In problem 3, you should show on your third graph where the regression line is. Check what your text says about normal probability plots and analize the plot you did. Explain the results of the t and F tests using a 5% significance level. (2)