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 data432.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.)

here is the data

obs     sat     act
1       975     23
2       1103    23
3       1004    19
4       1122    27
5       1014    27
6       1078    22
7       960     23
8       1054    20
9       835     18
10      1221    25
11      919     18
12      797     18
13      1087    22
14      757     20
15      1108    24
16      1029    24
17      883     19
18      1142    27
19      1131    25
20      863     19
21      1315    31
22      1137    25
23      998     23
24      714     9
25      416     7
26      720     15
27      1014    23
28      834     15
29      933     17
30      760     20
31      1022    21
32      874     16
33      1007    23
34      960     23
35      810     20
36      1085    24
37      755     20
38      942     20
39      960     23
40      1021    26
41      608     11
42      841     18
43      931     14
44      1183    26
45      996     26
46      953     21
47      1033    22
48      603     12
49      779     16
50      917     24
51      1060    25
52      633     12
53      687     16
54      915     20
55      927     20
56      855     22
57      721     12
58      997     25
59      760     15
60      859     20

Answer 1

a)

overall pattern seems linear with positive slope

applying regression on above data:

b)

applying regression:

Act =-2.876+0.025*SAT

t=13.428

p value =0.0000

c)

correlation between the two tests =0.870