Question

DATA: obs sat act 1 979 21 2 1088 23 3 782 18 4 858 23 5 667 15 6 965 22 7 981 24 8 787 15 9 828 17 10 902 19 11 1040 19 12 965 26 13 977 21 14 938 20 15 1034 25 16 1161 26 17 833 17 18 715 16 19 1219 27 20 696 19 21 678 16 22 779 15 23 1309 32 24 613 18 25 810 18 26 966 23 27 966 21 28 1253 31 29 823 17 30 1153 23 31 1048 20 32 1015 26 33 602 11 34 769 17 35 891 20 36 835 18 37 925 18 38 1203 28 39 992 19 40 1007 26 41 978 22 42 903 17 43 1084 30 44 730 17 45 1253 28 46 650 10 47 1138 23 48 845 18 49 870 18 50 1125 27 51 863 15 52 1132 22 53 960 17 54 590 14 55 1181 23 56 774 17 57 1139 26 58 910 20 59 659 14 60 942 20

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 below 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.)

Answer 1

(a)

Following is the scatter plot of the data:

(b)

Following is the output of regression analysis:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.867371812
R Square	0.75233386
Adjusted R Square	0.748063755
Standard Error	2.407124627
Observations	60
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1020.866893	1020.866893	176.186232	3.16176E-19
Residual	58	336.0664403	5.79424897
Total	59	1356.933333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-1.061499562	1.651391489	-0.642790985	0.522892803	-4.367118751	2.244119627
sat, x	0.023157696	0.001744654	13.27351619	3.16176E-19	0.019665391	0.026650001

Following is the scatter plot with regression analysis:

The required regression analysis is

Act = -1.061 + 0.023* Sat

The test statistics is :

t = 13.27

The p-value is : 0.0000

Since p-value is less than 0.05 so we reject the null hypothesis. That slope is significant to the model.

(c)

The correlation coefficient is

r = 0.867