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 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.)

DATA

obs     sat     act
1       855     22
2       592     10
3       1044    26
4       1064    22
5       1159    28
6       644     16
7       875     17
8       789     22
9       1070    16
10      981     24
11      901     15
12      740     16
13      652     14
14      861     18
15      1027    20
16      901     19
17      827     13
18      1043    27
19      722     11
20      602     15
21      1011    18
22      598     12
23      778     15
24      888     22
25      643     15
26      1118    22
27      1085    27
28      1053    31
29      721     14
30      805     20
31      1022    25
32      582     11
33      1065    24
34      1219    23
35      846     18
36      1061    25
37      807     16
38      1288    26
39      855     22
40      840     19
41      1006    20
42      931     19
43      770     17
44      725     19
45      954     23
46      672     11
47      481     11
48      974     17
49      814     18
50      656     12
51      687     19
52      966     21
53      913     17
54      1070 27
55      778     15
56      686     14
57      904     20
58      957     23
59      875     23
60      974     22

Answer 1