Based on a sample of n=15, the least-squares method was used to develop the prediction line Yi=6+2Xi. In addition, SYX=1.5, X=3 and ∑i=1nXi−X2=15. Complete parts (a) and (b) below.
Based on a sample of n=15, the least-squares method was used to develop the prediction line Yi=6+2Xi. In addition, SYX=1.5, X=3 and ∑i=1nXi−X2=15. Complete parts (a) and (b) below.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Based on a sample of
n=15,
the least-squares method was used to develop the prediction line
Yi=6+2Xi.
In addition,
SYX=1.5,
X=3
and
∑i=1nXi−X2=15.
Complete parts (a) and (b) below.Click here to view page 1 of the table of the critical values of t.
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Click here to view page 2 of the table of the critical values of t.
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a. Construct a
interval estimate of the population mean response for X=2.
90%
confidence enter your response here≤μY|X=2≤enter your response here
(Round to two decimal places as needed.)
b. Construct a
90%
prediction interval of an individual response for
X=2.
enter your response here≤YX=2≤enter your response here
(Round to two decimal places as needed.)
Transcribed Image Text:Upper-tail areas
Degrees of
freedom
0.25
0.10
0.05
0.025
0.01
0.005
1.0000
0.8165
63138
3.0777
1.8856
1.6377
1.5332
12.7062
4.3027
3.1824
2.7764
2.5706
31.8207
6.9646
4.5407
3.7469
63.6574
9.9248
5.8409
4.6041
2.9200
2.3534
3
4
0.7649
0.7407
2.1318
0.7267
1.4759
2.0150
3.3649
4.0322
6.
0.7176
0.7111
0.7064
0.7027
0.6998
1.4398
1.4149
1.3968
1.3830
1.3722
1.9432
1.8946
1.8595
1.8331
1.8125
2.4469
2.3646
2.3060
2.2622
2.2281
3.1427
2.9980
2.8965
2.8214
2.7638
3.7074
3.4995
3.3554
3.2498
3.1603
10
11
12
13
14
15
0.6974
0.6955
0.6038
0.6924
0.6912
1.3634
1.3562
1.3502
1.3450
1.3406
1.7959
1.7823
1.7709
1.7613
1.7531
2.2010
2.1788
2.1604
2.1448
2.1315
2.7181
2.6810
2.6503
2.6245
2.6025
3.1058
3.0545
3.0123
2.9768
2.9467
16
17
18
19
0.6001
0.6892
0.6884
0.6876
1.3368
1.3334
1.3304
1.3277
1.7459
1.7396
1.7341
1.7291
2.1199
2.1098
2.1009
2.0930
2.5835
2.5669
2.5524
2.5395
2.9208
2.8982
2.8784
2.8609
20
0.6870
1.3253
1.7247
2.0860
2.5280
2.8453
21
0.6864
1.3232
1.7207
2.0796
2.5177
2.8314
2.5083
2.4999
22
23
24
25
0.6858
0.6853
0.6848
0.6844
1.3212
1.3195
1.3178
1.3163
1.7171
1.7139
1.7109
1.7081
2.0739
2.0687
2.0639
2.8188
2.8073
2.7969
2.7874
2.4922
2.4851
2.0595
26
27
28
29
30
0.6840
0.6837
0.6834
1.7056
1.7033
2.0555
2.4786
2.4727
2.4671
2.7787
2.7707
2.7633
2.7564
2.7500
1.3150
2.0518
2.0484
2.0452
2.0423
1.3137
1.3125
1.7011
1.3114
1.3104
1.6991
1.6973
2.4620
2.4573
0.6830
0.6828
31
32
33
34
0.6825
0.6822
1.3095
1.3086
1.3077
1.3070
1.6955
1.6939
1.6924
1.6909
2.0395
2.0369
2.0345
2.0322
2.4528
2.4487
2.4448
2.4411
2.7740
2.7385
2.7333
2.7284
0.6820
0.6818
35
0.6816
1.3062
1.6896
2.0301
2.4377
2.7238
36
0.6814
1.3055
1.6883
2.0281
2.0262
2.0244
2.0227
2.4345
2.7195
37
38
0.6812
1.3049
1.6871
2.4314
2.7154
0.6810
1.3042
1.6860
2.4286
2.4258
2.4233
2.7116
39
0.6808
1.3036
1.3031
1.6849
2.7079
40
0.6807
1.6839
2.0211
2.7045
41
42
43
44
45
0.6805
0.6804
0.6802
0.6801
0.6800
1.3025
1.3020
1.3016
1.3011
1.3006
1.6829
1.6820
1.6811
1.6802
1.6794
2.0195
2.0181
2.0167
2.0154
2.0141
2.4208
2.4185
2.4163
2.4141
2.4121
2.7012
2.6981
2.6951
2.6923
2.6896
1.6787
2.0129
2.0117
2.4102
46
47
48
0.6799
0.6797
0.6796
1.3022
1.2998
1.2994
1.6779
1.6772
2.6870
2.6846
2.4083
2.0106
2.4066
2.6822
Degrees of
freedom
0.25
0.10
0.05
0.025
0.01
0.005
Upper-tail areas
Transcribed Image Text:Degrees of
freedom
0.25
0.10
0.05
0.025
0.01
0.005
49
50
0.6795
0.6794
1.2991
1.2987
1.6766
1.6759
2.0096
2.0086
2.4049
2.4033
2.6800
2.6778
51
52
53
54
55
0.6793
0.6792
0.6791
0.6791
0.6790
1.2984
1.2980
1.2977
1.2974
1.2971
1.6753
1.6747
1.6741
1.6736
1.6730
1.6725
1.6720
1.6716
1.6711
1.6706
2.0076
2.0066
2.0057
2.0049
2.0040
2.4017
2.4002
2.3988
2.3974
2.3961
2.6757
2.6737
2.6718
2.6700
2.6682
0.6789
0.6788
0.6787
0.6787
0.6786
1.2969
1.2966
1.2963
1.2961
1.2958
2.0032
2.0025
2.0017
2.0010
2.0003
2.3948
2.3936
2.3924
2.3912
2.3901
2.6665
2.6649
2.6633
2.6618
2.6603
57
58
60
0.6785
0.6785
0.6784
0.6783
0.6783
1.2956
1.2954
1.2951
1.2949
1.2947
1.6702
1.6698
1.6604
1.6600
1.6686
1.9906
1.9990
1.9983
1.9977
1.9971
2.3890
2.3880
2.3870
2.3860
2.3851
2.6589
2.6575
2.6561
2.6549
2.6536
65
0.6782
0.6782
0.6781
0.6781
1.2945
1.2943
1.2941
1.2939
1.2938
1.6683
1.6679
1.6676
1.6672
1.6669
1.9966
68
69
70
1.9960
1.9955
1.9949
2.3842
2.3833
2.3824
2.3816
2.3808
2.6524
2.6512
2.6501
2.6490
2.6479
0.6780
1.9944
71
72
73
74
0.6780
0.6779
0.6779
0.6778
0.6778
1.2936
1.2934
1.2933
1.2931
1.6666
1.6663
1.6660
1.6657
1.6654
1.9939
1.9935
1.9930
1.9925
1.9921
2.3800
2.3793
2.3785
2.3778
2.3771
2.6469
2.6459
2.6449
2.6439
2.6430
1.2929
0.6777
0.6777
0.6776
0.6776
0.6776
1.2928
1.2926
1.2925
1.2924
1.2922
1.6652
1.6649
1.6646
1.9917
1.9913
1.9908
1.9905
2.3764
2.3758
2.3751
2.3745
2.3739
2.6421
2.6412
2.6403
2.6395
2.6387
79
1.6644
1.6641
1.9901
0.6775
0.6775
0.6775
0.6774
0.6774
1.2921
1.2920
1.2918
1.2917
1.2916
1.6639
1.6636
1.6634
1.6632
1.6630
1.9897
1.9893
1.9890
1.9886
2.3733
2.3727
2.3721
2.3716
2.3710
2.6379
2.6371
2.6364
2.6356
2.6349
1.9883
0.6774
0.6773
0.6773
0.6773
0.6772
1.2915
1.2914
1.2912
1.2911
1.2910
1.6628
1.6626
1.6624
1.9879
1.9876
1.9873
1.9870
1.9867
2.3705
2.3700
2.3695
2.6342
2.6335
2.6329
2.6322
2.6316
1.6622
1.6620
2.3690
2.3685
0.6772
0.6772
0.6771
0.6771
0.6771
91
1.2909
1.2908
1.2907
1.2906
1.2905
1.6618
1.6616
1.6614
1.9864
1.9861
1.9858
1.9855
1.9853
2.3680
2.3676
2.3671
2.3667
2.3662
2.6309
2.6303
2.6297
2.6291
2.6286
93
94
1.6612
1.6611
95
1.9850
1.9847
1.9845
1.9842
1.9840
96
97
0.6771
0.6770
0.6770
1.2904
1.2903
1.2902
1.2902
1.6609
2.3658
2.3654
2.3650
2.6280
2.6275
2.6269
2.6264
1.6607
1.6606
98
99
0.6770
0.6770
1.6604
1.6602
2.3646
2.3642
100
1.2901
2.6259
110
0.6767
1.2893
1.6588
1.9818
2.3607
2.6213
0.6765
0.6745
120
1.2886
1.6577
1.9799
2.3578
2.6174
1.2816
16449
1.9600
2.3263
2.5758
Degrees of
freedom
0.25
0.10
0.05
0.025
0.01
0.005
Upper-tail areas
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