Question

Performance Data
Group	Test 1	Test 2
1	96	85
1	96	88
1	91	81
1	95	78
1	92	85
1	93	87
1	98	84
1	92	82
1	97	89
1	95	96
1	99	93
1	89	90
1	94	90
1	92	94
1	94	84
1	90	92
1	91	70
1	90	81
1	86	81
1	90	76
1	91	79
1	88	83
1	87	82
0	93	74
0	90	84
0	91	81
0	91	78
0	88	78
0	86	86
0	79	81
0	83	84
0	79	77
0	88	75
0	81	85
0	85	83
0	82	72
0	82	81
0	81	77
0	86	76
0	81	84
0	85	78
0	83	77
0	81	71

A different teacher wants to see if Test 1 was predictive of Test 2. Please answer the following questions based on the data set.

A) What is the y intercept?

B) What is the slope?

C) What is the amount of variance explained in Test 2 by Test 1?

D) Assuming a student got an 84 on Test 1, what is the predicted score for Test 2? Please round to the nearest whole number.

E). For the Excel Data Set please find and report for Test 1 and Test 2 the Mean, SD, and the tolerance levels for both for which there would be any outliers (i.e., the value for which a score must be less than to be consider an outlier and the value for which a number must greater than to be considered an outlier.

Answer 1

Sol:

Peform regression in excel

Data >Data analysis >Regression

Test1 as X

Test 2 as Y

click ok

Output

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.450532
R Square	0.202979
Adjusted R Square	0.18354
Standard Error	5.519503
Observations	43
ANOVA
	df	SS	MS	F	Significance F
Regression	1	318.1015	318.1015	10.44157	0.002432
Residual	41	1249.061	30.46491
Total	42	1567.163
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	37.11728	13.95839	2.659137	0.011124	8.927732	65.30682
Test1	0.506662	0.156796	3.231342	0.002432	0.190006	0.823319

A) What is the y intercept?

y intercept=37.11728

B) What is the slope?

slope=0.506662

C) What is the amount of variance explained in Test 2 by Test 1?

R sq=0.202979

=20.3%

20.3% varaince in Test 2 is explained by Test1

D) Assuming a student got an 84 on Test 1, what is the predicted score for Test 2? Please round to the nearest whole number.

we have

Test2=37.11728+ 0.506662*test1

for test 1=84,predicted test 2

Test2=37.11728+ 0.506662*84

Test2= 79.67689

Test 2=80

predicted score for Test 2=80

Solution-E

fivenumber sumamry for test 1

Fivenum syummary is MIN,Q1,Q2,Q3,MAX

79.0 85.0 90.0 92.5 99.0

IQR=Q3-Q1=92.5-85.0=7.5

lower fence

Q-1.5IQR

85.0-1.5*7.5

=73.75

values below 73.75 are outliers

upper fence

Q3+1.5IQR

fivenumber sumamry for test 2

70 78 82 85 96

IQR=Q3-Q1=85-78=7

lower fence

Q-1.5IQR

78-1.5*7

= 67.5

upper fence

=Q3+1.5IQR

85+1.5*7

= 95.5

Test1		Test2
Mean	88.86046512	Mean	82.13953
Standard Error	0.828333659	Standard Error	0.931533
Lower fence	73.75	Lower fence	67.5
Upper fence	103.75	Upper fence	95.5