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 data297.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       846     15
2       713     19
3       647     13
4       1092    23
5       798     18
6       623     14
7       896     19
8       828     21
9       641     13
10      1038    22
11      715     13
12      872     19
13      867     25
14      776     18
15      824     19
16      935     22
17      848     17
18      497     15
19      627     12
20      911     17
21      1024    23
22      699     15
23      1046    27
24      866     19
25      1114    29
26      1004    20
27      771     20
28      738     16
29      822     23
30      757     16
31      946     21
32      721     15
33      1066    21
34      1051    24
35      691     16
36      861     14
37      836     18
38      706     19
39      785     15
40      964     19
41      1080    25
42      893     22
43      1039    25
44      802     17
45      543     15
46      1135    22
47      963     24
48      538     10
49      770     19
50      994     22
51      1303    29
52      492     8
53      921     18
54      850     18
55      609     12
56      848     21
57      963     17
58      841     14
59      1068 24
60      1131 25

Answer 1