The SAT and the ACT are the two major standardized tests that colleges use to evaluate candidates. Most students take just one of these tests. However, some students take both. The data data18.dat gives the scores of 60 students who did this. How can we relate the two tests?
(a) Plot the data with SAT on the x axis and ACT on the
y axis. Describe the overall pattern and any unusual
observations.
(b) Find the least-squares regression line and draw it on your
plot. Give the results of the significance test for the slope.
(Round your regression slope and intercept to three decimal places,
your test statistic to two decimal places, and your
P-value to four decimal places.)
ACT = | + (SAT) |
t = | |
P = |
(c) What is the correlation between the two tests? (Round your
answer to three decimal places.)
obs sat act 1 715 17 2 804 18 3 537 9 4 1122 23 5 745 17 6 1110 23 7 1028 23 8 1031 26 9 881 23 10 856 15 11 841 11 12 829 19 13 931 22 14 1013 22 15 722 20 16 839 17 17 795 13 18 865 15 19 1007 22 20 603 17 21 1028 26 22 794 18 23 950 26 24 808 13 25 809 14 26 699 10 27 568 12 28 1155 27 29 981 24 30 890 19 31 628 15 32 1084 23 33 931 20 34 1051 18 35 990 19 36 1151 25 37 605 16 38 758 21 39 871 14 40 645 14 41 945 21 42 1034 28 43 820 23 44 943 26 45 982 19 46 441 10 47 800 14 48 902 18 49 864 23 50 349 6 51 1122 27 52 585 15 53 845 18 54 681 11 55 1325 29 56 1023 28 57 614 13 58 1005 20 59 756 20 60 691 12
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