Question

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 data141.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 1 817 19 2 691 13 3 1027 23 4 1050 24 5 947 18 6 918 15 7 641 14 8 823 22 9 746 14 10 874 16 11 1054 22 12 915 14 13 774 23 14 1218 27 15 742 17 16 1095 24 17 954 21 18 1035 25 19 927 23 20 1147 23 21 540 11 22 1017 22 23 826 20 24 1014 20 25 615 18 26 661 14 27 872 19 28 679 17 29 931 23 30 644 13 31 787 14 32 390 13 33 780 19 34 875 17 35 1086 21 36 987 22 37 659 17 38 930 15 39 1042 20 40 981 22 41 725 21 42 967 24 43 946 22 44 1143 27 45 918 19 46 1192 24 47 833 17 48 882 22 49 712 19 50 1122 20 51 982 21 52 809 18 53 772 19 54 850 17 55 554 7 56 811 14 57 1043 23 58 921 20 59 1001 27 60 872 20

Answer #1

a)

scatter plot is attached above ; whcih shows there is a linear relationship between SAT and ACT score

b)

least square line is drawn on scatter plot

ACt score =2.939+0.019*SAT score

test statistic t =8.920

p value =0.000

c)correlation coefficient =0.7605 ~0.761

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5
15
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12
23
22
14
19
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21
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10
18
13
y
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24
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14
28
21
22
20
21
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achievement score, y (measured by a comprehensive final),
were measured for 20 students in a beginning computer-science
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3
17
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14
21
20
14
19
18
15
17
16
9
7
4
21
19
10
20
13
y
19
19
24
36
27
26
25
28
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27
21
24
18
18
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28
21
22
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