CORRELATION AND SIMPLE LINEAR REGRESSION

IQ	TEST SCORE	X1*X2	IQ2	TS2
106	16	1696	11236	256
118	21	2478	13924	441
80	10	800	6400	100
120	25	3000	14400	625
117	16	1872	13689	256
94	11	1034	8836	121
106	6	636	11236	36
119	32	3808	14161	1024
107	20	2140	11449	400
128	15	1920	16384	225
122	26	3172	14884	676
116	18	2088	13456	324
1333	216	24644	150055	4484

Test 2 Self test I

pearson product-moment coefficient of correlation

rxy= 1

Rxy = 12(24644)-[( 1333)(216)]/ ⁄(12*150055)-(1333)²] [(12*4484)-(216)²]

     = 0.598215

The above result indicates tha there is a moderate  direct relationship between I Q and methemathical test Score . This implies hat as IQ increases Mathematical  moderately would increase  also.

B1 -           =  24644-(1333)(216)____   = 0.328

                                                    150055- (1333)²/12

Bo = Mean Y – bi meanX =   18- (0.328)(111.0833)  =  - 18.4499

The regression equation is                           

Mathematical Test Score  = -18.4499 + 0.328131 IQ

Se = Sy   = 7.36 x .80134   = 5.897

Approximately 68% of the samples will have a actual score that lie within the Se of their predicted scores YỸ +/- 5.897 = 18 +/- (5.897) . in other words 68% have scores within the range 12.103 to 23.897. Like wise, approximately 95% of the samples will have the actual scores that lie within two Se’s their predicted scores;18 +/- 11.794 or 6.206 to 29.794.

The regression equation is                           

Mathematical = -18.4499 + 0.328131 IQ                

                                                     

S = 6.18640      R-Sq = 35.8 %      R-Sq(adj) = 29.4 %

Analysis of Variance

Source            DF         SS         MS         F      P

Regression         1    213.285    213.285   5.57295  0.040

Error             10    382.715     38.271                

Total             11    596.000                           

SELF Test 1

No 1

sample	Gen Ave	Applitude	X1*X2	x12	x22
1	93	94	8742	8649	8836
2	88	82	7216	7744	6724
3	87	90	7830	7569	8100
4	89	87	7743	7921	7569
5	84	86	7224	7056	7396
6	82	85	6970	6724	7225
7	80	76	6080	6400	5776
8	91	86	7826	8281	7396
9	87	80	6960	7569	6400
10	86	81	6966	7396	6561
11	81	84	6804	6561	7056
12	88	80	7040	7744	6400
13	90	85	7650	8100	7225
14	82	84	6888	6724	7056
15	83	88	7304	6889	7744
total	1291	1268	109243	111327	107464

pearson product-moment coefficient of correlation

rxy= 1

Rxy = 15(109243)-[( 1291)(1268)]/ ⁄(15*111327)-(1291)²] [(15*107464)-(1268)²]

     = 0.453769

The above result indicates tha there is a moderate  direct relationship between General Average  and Applitude  test Score . This implies hat as General Average increases Applitude test score   moderately would increase  also.

Pearson correlation of C5 and C6 = 0.454

P-Value = 0.089

To madam Molina

a.X1 sex and X2 eduactional attainment

correlation used: Phi Coefficient

a	4		bc	6
b	3		ad	24
c	2		a+c	6
d	6		b+d	9
			a+b	7
			c+d	8

.rq =(6)-(24)

       __________    =   - 0.32733

           √3024

The relationship between sex and and educational attainment have definite but small negative correlation.

b. X1 sex and X3 type of employement

correlation used: Phi Coefficient

a	4		bc	16
b	4		ad	12
c	4		a+c	8
d	3		b+d	7
			a+b	8
			c+d	7

rq=(16)-(12)

       __________    =    0.0714

           √3136

The  result suggest that there is slight relationship between sex and type of employement

c. X2 Educational attainment and x3 Type of employement

correlation used: Phi Coefficient

a	4		bc	12
b	4		ad	16
c	3		a+c	7
d	4		b+d	8
			a+b	8
			c+d	7

Rq=  (12)-(16)

       __________    =    -0.07143

          √3136

The  result suggest that there is slight negative  relationship between type of employement and educational attainement

d. X2  educational attainment and x4 Rank in laedership qualities

correlation used: Rank biseral coefficient

sum with masters degree= 53 mean = 6.625

sum with out masters = 67 mean= 9.571

N= 15

Rs = 2/15 (6.625-9.571)

     = -0.3928

The realtionship between educational attainment and leadearship qualitiies have slight but not definite or can be also considered as aweak relationship.

e. X2 educational attainment and x6  verbal applitude

correlation used: point biseral coefficient

mean w1= 86.5            N1= 8

mean x6= 84.6             No= 7

SD of x6= 6.684          N = 15

.rpb      = 86.5-84.6/6.684 [√8(15)/7(14)

             = 0.314

A slight but not definite relationship is being considered in terms of the relationship between eduactional attainment and verbal applitude

f. x4 rank in leadership qualities and x5 rank in creativity test

correlation used: spearman rho correlation coefficient

x4	x5		X4-x5	(x4-x5)2
9	6		3	9		696
13	7		-4	16		225
1	5		-4	16		3360
12	14		-2	4		0.207143
7	10		-3	9		0.792857
8	8		0	0
2	4		-2	4
11	13		-2	4
15	11		4	16
10	9		1	1
4	1		3	9
5	3		2	4
14	12		2	4
13	15		-2	4
6	2		4	16
				116

Rs = 1- 6 Ƹ(116)/15(15²-1)

     = 0.793

The relationship between the two ranks are substantial we can say as their leadership increase their creativity also increase

G X4 rank in leadership qualities  and X6 verbal applitude

correlation used: spearman rho correlation coefficient

x4	x6	x6 ranked	x-y	(x-y)2
9	90	12.5	-3.5	12.25	5475
3	88	10	-7	49	225
1	85	7	-6	36	3360
12	86	8	4	16	1.629464
7	82	5	2	4	-0.62946
8	90	12.5	-4.5	20.25
2	89	11	-9	81
11	83	6	5	25
15	80	4	11	121
10	78	3	7	49
4	95	15	-11	121
5	91	14	-9	81
14	75	2	12	144
13	70	1	12	144
6	87	9	-3	9
				912.5

Rs = 1- 6 Ƹ(912.5)/15(15²-1)

     = -0.629

The relationship between the two ranks are substantial and inversely proportional as their leadership skill goes up their applitude substantialy goes down.

h. X5 rank in creativity and X6 verbal applitude

correlation used: spearman rho correlation coefficient

x5	x6	Rankedx6	x-y	(x-y)2
6	90	12.5	-6.5	42.25	5889
7	88	10	-3	9	225
5	85	7	-2	4	3360
14	86	8	6	36	1.752679
10	82	5	5	25	-0.75268
8	90	12.5	-4.5	20.25
4	89	11	-7	49
13	83	6	7	49
11	80	4	7	49
9	78	3	6	36
1	95	15	-14	196
3	91	14	-11	121
12	75	2	10	100
15	70	1	14	196
2	87	9	-7	49
				981.5

Rs = 1- 6 Ƹ(981.5)/15(15²-1)

     = -0.7526

The realtionship between rank increativity and verbal applitude are subtantially inversely proportional as the creatuvity increase the applitude decreases

.i X5 rank in creativity and X7 numerical proficiency

correlation used: spearman rho correlation coefficient

x5	X7	ranked	x-y	(x-y)2
6	89	13	-7	49	4773
7	87	11	-4	16	225
5	83	7.5	-2.5	6.25	3360
14	85	9.5	4.5	20.25	1.420536
10	90	14	-4	16	-0.42054
8	85	9.5	-1.5	2.25
4	81	5.5	-1.5	2.25
13	79	4	9	81
11	75	1	10	100
9	76	2	7	49
1	93	15	-14	196
3	88	12	-9	81
12	83	7.5	4.5	20.25
15	77	3	12	144
2	81	5.5	-3.5	12.25
				795.5

Rs = 1- 6 Ƹ(795.5)/15(15²-1)

     = -0.420

The corellation of ranked in creativity and numerical proficientcy are in moderate category somehow creativity have effect on numerical proficiency indirectly or inversly proportional as creativity increase numerical proficiency moderately decrease.

j. X6  verbal applitude and X7 numerical profficiency

pearson product-moment coefficient of correlation

x6	x7	x6*x7	x62	x72
90	89	8010	8100	7921
88	87	7656	7744	7569
85	83	7055	7225	6889
86	85	7310	7396	7225
82	90	7380	6724	8100
90	85	7650	8100	7225
89	81	7209	7921	6561
83	79	6557	6889	6241
80	75	6000	6400	5625
78	76	5928	6084	5776
95	93	8835	9025	8649
91	88	8008	8281	7744
75	83	6225	5625	6889
70	77	5390	4900	5929
87	81	7047	7569	6561
1269	1252	106260	107983	104904

Rxy = 15(106260)-[( 1269)( 1252)]/ √[(15*107983)-(1269)²] [(15*104904)-(1252)²]

     = 0.678116

The above result indicates tha there is a substantial direct relationship between . X6  verbal applitude and X7 numerical profficiency. This implies hat as verbal applitude increases numerical proficiency substantially increase also.

Analysis of Variance

Source     DF        SS        MS        F        P

Factor      2     186.2      93.1     3.37    0.049

Error      27     745.8      27.6

Total      29     932.0

                                   Individual 95% CIs For Mean

                                   Based on Pooled StDev

Level       N      Mean     StDev  -+---------+---------+---------+-----

C9         10    24.900     7.078              (---------*---------)

C10        10    26.500     3.923                   (---------*--------)

C11        10    20.600     4.169  (---------*---------)