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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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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
90​%
confidence interval estimate of the population mean response for X=2.
 
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.)
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: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
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
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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