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 data25.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       882     19
2       993     21
3       1172    23
4       800     12
5       845     19
6       1015    22
7       862     20
8       860     23
9       635     17
10      962     18
11      1004    26
12      840     15
13      1023    21
14      1134    23
15      642     15
16      920     21
17      842     18
18      820     16
19      889     22
20      815     17
21      570     14
22      1107    24
23      984     21
24      721     20
25      1026    17
26      748     17
27      972     19
28      912     20
29      857     13
30      905     18
31      1076    22
32      1151    26
33      488     12
34      789     13
35      986     21
36      697     17
37      780     17
38      964     25
39      1019    30
40      1003    26
41      666     10
42      1061    25
43      1106    26
44      1151    24
45      705     17
46      1018    27
47      881     20
48      1192    26
49      750     17
50      824     16
51      762     23
52      615     11
53      855     19
54      1022    22
55      1018    23
56      759     18
57      813     21
58      965     22
59      1046    26
60      1018    21

Answer 1