In: Statistics and Probability
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 data42.datgives 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.)
Data set
obs sat act 1 708 15 2 1064 26 3 912 25 4 953 23 5 1251 28 6 648 12 7 1005 21 8 664 16 9 604 17 10 945 25 11 1034 21 12 895 16 13 935 19 14 909 24 15 938 17 16 777 21 17 703 14 18 1242 25 19 971 21 20 817 17 21 885 18 22 1138 23 23 909 17 24 788 21 25 1064 19 26 1170 26 27 806 15 28 923 20 29 1170 21 30 579 16 31 888 22 32 1207 24 33 871 22 34 1117 25 35 1070 17 36 767 17 37 969 22 38 1027 30 39 931 23 40 933 21 41 965 26 42 960 22 43 787 17 44 1002 20 45 1221 33 46 1042 24 47 897 22 48 1061 24 49 898 18 50 720 11 51 976 18 52 1066 25 53 931 18 54 593 12 55 735 16 56 544 10 57 871 17 58 875 21 59 921 22 60 559 15