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 data163.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.)

The data is below

obs     sat        act
1       1201    26
2       462     11
3       1085    24
4       973     22
5       974     20
6       889     20
7       1071    20
8       634     14
9       940     18
10      760     16
11      830     22
12      1165    25
13      743     19
14      1061    24
15      987     26
16      1162    20
17      1149    29
18      658     18
19      1016    22
20      942     22
21      716     15
22      1205    29
23      659     12
24      895     20
25      629     17
26      815     16
27      1000    23
28      764     17
29      620     11
30      812     16
31      908     19
32      720     17
33      977     22
34      722     16
35      841     18
36      1254    27
37      1256    27
38      1085    26
39      1143    26
40      1189    26
41      983     22
42      814     20
43      1143    26
44      816     16
45      931     21
46      737     16
47      763     18
48      1064    24
49      619     14
50      1013    23
51      776     18
52      622     11
53      1036    23
54      593     14
55      1026    22
56      706     18
57      715     15
58      1266    28
59      839     15
60      884     16

Answer 1