b) Dependent variable, y. (Give units of measurement, e.g., inches, dollars, mil
ID: 3153977 • Letter: B
Question
b) Dependent variable, y. (Give units of measurement, e.g., inches, dollars, miles.) (2 pts.)
c) Independent quantitative variable, x1 . (Give units of measurement, e.g., inches, dollars, miles.) (2 pts.)
d) Independent qualitative variable, x2 (2 pts.) x2 = 1 if 0 if 2. When the independent variables are highly correlated
P.O. #1 Data Sheet
Student Edition of Statistix 10.0 connorcolettExam3.sx, 3/24/2016, 4:00:09 PM
CASE PTS GP ORIGIN GPORIGIN GPSQ GPSQORGN
1 92 74 1 74 5476 5476
2 82 74 1 74 5476 5476
3 76 71 1 71 5041 5041
4 75 75 0 0 5625 0
5 73 72 0 0 5184 0
6 73 72 1 72 5184 5184
7 71 72 1 72 5184 5184
8 70 73 1 73 5329 5329
9 69 73 1 73 5329 5329
10 67 72 0 0 5184 0
11 65 69 0 0 4761 0
12 65 73 1 73 5329 5329
13 64 70 0 0 4900 0
14 64 72 0 0 5184 0
15 64 73 1 73 5329 5329
16 63 72 0 0 5184 0
17 62 72 1 72 5184 5184
18 61 69 1 69 4761 4761
19 60 73 1 73 5329 5329
20 60 73 1 73 5329 5329
21 60 71 0 0 5041 0
22 58 57 0 0 3249 0
23 58 72 0 0 5184 0
24 58 76 1 76 5776 5776
25 57 69 1 69 4761 4761
26 56 71 1 71 5041 5041
27 56 67 1 67 4489 4489
28 56 74 0 0 5476 0
29 56 70 1 70 4900 4900
30 55 72 1 72 5184 5184
31 55 68 1 68 4624 4624
32 55 62 1 62 3844 3844
33 55 69 1 69 4761 4761
34 55 70 0 0 4900 0
35 55 74 0 0 5476 0
36 54 72 1 72 5184 5184
37 54 64 0 0 4096 0
38 54 72 0 0 5184 0
39 54 73 0 0 5329 0
40 54 74 1 74 5476 5476
P.O. #2 SCATTERPLOT OF ACTUAL DATA
P.O. #3 CORRELATION MATRIX
Student Edition of Statistix 10.0 connorcolettexam3dat..., 3/24/2016, 4:33:53 PM
Correlations (Pearson)
PTS GP ORIGIN
PTS 1.0000
GP 0.3265 1.0000
ORIGIN 0.1261 0.1074 1.0000
Cases Included 40 Missing Cases 0
P.O. #4 MODEL #1
Student Edition of Statistix 10.0 connorcolettexam3dat..., 3/24/2016, 4:46:51 PM
Least Squares Linear Regression of PTS Points
Predictor
Variables Coefficient Std Error T P VIF
Constant 168.563 410.873 0.41 0.6842 0.0
GP -3.70721 12.4952 -0.30 0.7685 1046.9
GPSQ 0.03081 0.09438 0.33 0.7461 1087.4
ORIGIN 71.0044 765.452 0.09 0.9266 76199.6
GPORIGIN -2.86677 22.4413 -0.13 0.8991 334617.0
GPSQORGN 0.02659 0.16417 0.16 0.8723 92439.2
R² 0.1628 Mean Square Error (MSE) 73.8167
Adjusted R² 0.0397 Standard Deviation 8.59167
AICc 183.06
PRESS 4302.8
Source DF SS MS F P
Regression 5 488.21 97.6412 1.32 0.2780
Residual 34 2509.77 73.8167
Total 39 2997.98
Lack of Fit 13 849.94 65.3797 0.83 0.6301
Pure Error 21 1659.83 79.0397
Cases Included 40 Missing Cases 0
P.O. #5 COMPARE MODEL #1 TO MODEL #2
Student Edition of Statistix 10.0 connorcolettexam3dat..., 3/24/2016, 4:47:56 PM
Best Subset Regression Models for PTS Points
Forced Independent Variables: (A)GP (B)ORIGIN (C)GPORIGIN
Unforced Independent Variables: (D)GPSQ (E)GPSQORGN
Adjusted AICc -
P Cp R Square Min AICc Resid SS F P(F) Model Variables
4 2.3 0.0854 177.67 2531.11 A B C
5 4.0 0.0665 180.14 2511.71 0.27 0.6063 A B C D
5 4.1 0.0642 180.23 2517.64 0.19 0.6678 A B C E
6 6.0 0.0397 183.06 2509.77 0.14 0.8659 A B C D E
Cases Included 40 Missing Cases 0
P.O. #6 COMPARE MODEL #2 to MODEL #4
Student Edition of Statistix 10.0 connorcolettexam3dat..., 3/24/2016, 4:49:30 PM
Least Squares Linear Regression of PTS Points
Predictor
Variables Coefficient Std Error T P VIF
Constant 34.9392 34.6919 1.01 0.3206 0.0
GP 0.36844 0.49075 0.75 0.4577 1.7
ORIGIN -70.6993 54.9494 -1.29 0.2064 412.3
GPORIGIN 1.01838 0.77274 1.32 0.1959 416.5
R² 0.1557 Mean Square Error (MSE) 70.3087
Adjusted R² 0.0854 Standard Deviation 8.38503
AICc 177.67
PRESS 3082.8
Source DF SS MS F P
Regression 3 466.86 155.621 2.21 0.1033
Residual 36 2531.11 70.3087
Total 39 2997.98
Lack of Fit 15 871.28 58.0853 0.73 0.7264
Pure Error 21 1659.83 79.0397
Cases Included 40 Missing Cases 0
P.O. #7 BEST MODEL
Student Edition of Statistix 10.0 connorcolettexam3dat..., 3/24/2016, 4:55:32 PM
Least Squares Linear Regression of PTS Points
Predictor
Variables Coefficient Std Error T P VIF
Constant 5.95674 27.0966 0.22 0.8272 0.0
GP 0.77918 0.38283 2.04 0.0490 1.0
ORIGIN 1.62855 2.74895 0.59 0.5572 1.0
R² 0.1150 Mean Square Error (MSE) 71.7088
Adjusted R² 0.0672 Standard Deviation 8.46810
AICc 176.93
PRESS 3120.3
Source DF SS MS F P
Regression 2 344.75 172.375 2.40 0.1044
Residual 37 2653.23 71.7088
Total 39 2997.98
Lack of Fit 16 993.39 62.0870 0.79 0.6854
Pure Error 21 1659.83 79.0397
Cases Included 40 Missing Cases 0
P.O. #8 PREDICTION/CONFIDENCE INTERVALS
Student Edition of Statistix 10.0 connorcolettexam3dat..., 3/24/2016, 5:05:51 PM
Predicted/Fitted Values of PTS
Lower Predicted Bound 44.585 Lower Fitted Bound 58.476
Predicted Value 62.128 Fitted Value 62.128
Upper Predicted Bound 79.670 Upper Fitted Bound 65.780
SE (Predicted Value) 8.6578 SE (Fitted Value) 1.8023
Unusualness (Leverage) 0.0453
Percent Coverage 95
Corresponding T 2.03
Predictor Values: GP=70.000, ORIGIN=1.0000
P.O. #9 LIST OF STANDARDIZED RESIDUALS
Student Edition of Statistix 10.0 connorcolettexam3dat..., 3/24/2016, 5:08:03 PM
CASE STDRES
1 3.1213415
2 1.8795174
3 1.6202165
4 1.5889436
5 1.4259119
6 1.0865922
7 0.8426549
8 0.5549798
9 0.4322498
10 0.6840777
11 0.573858
12 -0.05867
13 0.4029726
14 0.3131606
15 -0.1814
16 0.1895216
17 -0.255063
18 0.132179
19 -0.67232
20 -0.67232
21 -0.135375
22 0.4429844
23 -0.428674
24 -1.507308
25 -0.362292
26 -0.817004
27 -0.14853
28 -0.781209
29 -0.65088
30 -1.108843
31 -0.44501
32 0.7924162
33 -0.609527
34 -0.706211
35 -0.907128
36 -1.230812
37 -0.606438
38 -0.92323
39 -0.975769
40 -1.59759
P.O. #10 SCATTERPLOT OF RESIDUALS VS. QN-X
P.O. #11 SCATTERPLOT OF RESIDUALS VS. PREDICTED - Y
P.O. #12 GRAPH OF BEST MODEL
P.O. #13 STEM-AND-LEAF PLOT OF RESIDUALS
Student Edition of Statistix 10.0 connorcolettexam3dat..., 3/24/2016, 5:14:26 PM
Stem and Leaf Plot of STDRES
Leaf Digit Unit = 0.1 Minimum -1.5976
--1 5 represents -1.5 Median -0.1650
Maximum 3.1213
Depth Stem Leaves
2 -1 55
4 -1 21
15 -0 99987766666
(8) -0 44321110
17 0 113444
11 0 55678
6 1 04
4 1 568
1 2
1 2
1 3 1
40 cases included 0 missing cases
P.. #2 SCATTERPLOT OF ACTUAL DATA P.. #2 SCATTERPLOT OF ACTUAL DATA Scatter Plot of PTS vs GP Scatter Plot of PTS vs GP 93 85 85 ORIGIN FOREIGN 277 277 ORIGIN a69 NORT HAMER FOREIGN o 69 NORTHAMER 72 72 Games Played Games Played P.. #12 GRAPH OF BEST MODEL P.. #10 SCATTERPLOT OF RESIDUALS VS. QN-X Scatter Plot of PRED vs GP Scatter Plot of RESID vs GP 85 ORIGIN FOREIGN NORT HAMER 72 Games Played Games Played P.O. #13 STEM-AND-LEAF PLOT OF RESIDUALS P.. #11 SCATTERPLOT OF RESIDUALS VS. PREDICTED-Y Student Edition of Statistix 10.0 connorcolettexam3dat. .., 3/24/2016, 5:14:26 Scatter Plot of RESID vS PRED Stem and Leaf Plot of STDRES Leaf Digit Unit 0.1 --1 5 represents -1.5 Median -0.1650 Depth Stem Leaves -1 55 -1 21 -0 99987766666 -0 44321110 15 0 113444 0 55678 1 04 1 568 85 PRED 40 cases included 0 missing casesExplanation / Answer
a) A linear regression is being used to predict PTS, based on independent variables GP, ORIGIN, GPORIGIN, GPSQ and GPSQORGN
b) Dependent variable Y is PTS
c) Independent quantitative variale X1 is ORIGIN in the best model
d) Inependent qualitative variable X2 is GP in the best model
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