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 data5.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       950     17
2       719     19
3       648     17
4       905     22
5       1263    29
6       995     25
7       1184    25
8       672     13
9       882     17
10      1082    21
11      875     17
12      951     20
13      1045    22
14      679     19
15      794     18
16      722     16
17      1227    28
18      746     14
19      1145    27
20      716     19
21      1208    28
22      950     21
23      890     23
24      761     17
25      969     17
26      647     11
27      857     21
28      991     21
29      798     17
30      666     14
31      761     19
32      660     20
33      631     16
34      1121    26
35      978     26
36      883     18
37      807     18
38      895     19
39      1184    23
40      869     17
41      582     14
42      1070    20
43      642     16
44      937     23
45      1086    27
46      1013    26
47      713     19
48      1144    25
49      990     24
50      878     16
51      870     26
52      1090    27
53      1095    26
54      781     19
55      1046    21
56      675     13
57      1257    25
58      1099    27
59      620     10
60      714     13

Answer 1

In excel select the data

Insert>scatter

You will get

click on axis title ,chart title

click on style to change it to required

you will get

Solution-b

In excel go to data>data analysis >regression

you will get

From regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.834051
R Square	0.695641
Adjusted R Square	0.690394
Standard Error	2.640571
Observations	60
ANOVA
	df	SS	MS	F	Significance F
Regression	1	924.3216	924.3216	132.5645	1.29E-16
Residual	58	404.4117	6.972616
Total	59	1328.733
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1.302955	1.679134	0.775968	0.44092	-2.0582	4.664107
sat	0.021023	0.001826	11.51367	1.29E-16	0.017368	0.024678

From output:

ACT=1.303+0.021*SAT

t=11.51

p=0.0000

Solutionc:

In excel

go to data>data analysis >correlation

From correlation matrix you get r=0.834

	sat	act
sat	1
act	0.834051	1

ANSWER:

r=0.834