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 data18.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       715       17
2       804       18
3       537       9
4       1122  23
5       745       17
6       1110  23
7       1028  23
8       1031  26
9       881       23
10      856       15
11      841       11
12      829       19
13      931       22
14      1013  22
15      722       20
16      839       17
17      795       13
18      865       15
19      1007  22
20      603       17
21      1028  26
22      794       18
23      950       26
24      808       13
25      809       14
26      699       10
27      568       12
28      1155  27
29      981       24
30      890       19
31      628       15
32      1084  23
33      931       20
34      1051  18
35      990       19
36      1151  25
37      605       16
38      758       21
39      871       14
40      645       14
41      945       21
42      1034  28
43      820       23
44      943       26
45      982       19
46      441       10
47      800       14
48      902       18
49      864       23
50      349       6
51      1122  27
52      585       15
53      845       18
54      681       11
55      1325  29
56      1023  28
57      614       13
58      1005  20
59      756       20
60      691       12

Answer 1