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 data141.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       817     19
2       691     13
3       1027    23
4       1050    24
5       947     18
6       918     15
7       641     14
8       823     22
9       746     14
10      874     16
11      1054    22
12      915     14
13      774     23
14      1218    27
15      742     17
16      1095    24
17      954     21
18      1035    25
19      927     23
20      1147    23
21      540     11
22      1017    22
23      826     20
24      1014    20
25      615     18
26      661     14
27      872     19
28      679     17
29      931     23
30      644     13
31      787     14
32      390     13
33      780     19
34      875     17
35      1086    21
36      987     22
37      659     17
38      930     15
39      1042    20
40      981     22
41      725     21
42      967     24
43      946     22
44      1143    27
45      918     19
46      1192    24
47      833     17
48      882     22
49      712     19
50      1122    20
51      982     21
52      809     18
53      772     19
54      850     17
55      554     7
56      811     14
57      1043    23
58      921     20
59      1001    27
60      872     20

Answer 1

a)

scatter plot is attached above ; whcih shows there is a linear relationship between SAT and ACT score

b)

least square line is drawn on scatter plot

ACt score =2.939+0.019*SAT score

test statistic t =8.920

p value =0.000

c)correlation coefficient =0.7605 ~0.761