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 data478.dat gives the scores of 60 students who did this. How can we relate the two tests?

obs     sat     act
1       736     16
2       958     17
3       787     17
4       626     16
5       887     16
6       1152 20
7       888     23
8       862     23
9       1276 26
10      903     19
11      720     16
12      1108 25
13      723     14
14      933     20
15      1332 28
16      1070 23
17      878     21
18      832     20
19      624     17
20      757     16
21      727     14
22      751     14
23      1158 23
24      905     21
25      993     22
26      669     15
27      468     11
28      926     18
29      553     13
30      1006 21
31      805     13
32      801     15
33      1191 20
34      1230 29
35      1043 24
36      687     17
37      769     19
38      864     21
39      748     16
40      1036 20
41      991     21
42      1000 20
43      698     16
44      1032 26
45      723      22
46      647      8
47      1288 27
48      856     19
49      557     14
50      901     21
51      814     16
52      789     14
53      885     23
54      692     15
55      1059 25
56      1198 27
57      1047 23
58      815      19
59      1223 22
60      1110 28

(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.)

Answer 1