Does being born closer to the school cut-off date affect school achievement?

I will record at least thirty students' (from the fourth grade) birthdays as well as how each student scores on the NECAP test. The birthdays and NECAP scores will be obtained from the school administration. I will plot the range of birthdays starting with January 1st (school cut-off date) and compare them to the numbers plotted from the NECAP scores in order to analyze any relationship. My prediction is that the closer the student is born to the school cut-off date the higher his/her scores will be. My thought is that the closer the child is born to the cut-off date the older they are hence more mature they would be once began school. Being that these older children would be in some cases much older then their classmates they would excel earlier and be given more opportunities to grow by placement in elite math groups, reading groups, classes for the gifted, etc. I believe these opportunities would continually produce a much more "gifted" child while those born significantly further from the cut-off date would require more time to develop and therefore be seen as average or less and given less opportunity to grow. Lurking variables may be a student who has been held back (as they may be older and born further from the cut-off date), students with disabilities (learning, physical, or emotional), and the state of the child when he/she took the NECAP test (they may have been tired, sick,etc.).

The three variables are: # of days student is born relative to the cut-off date and scores on the NECAP test (Reading and Math).

The Correlation Coefficient of Days From Cut-Off and Math Scores = -0.18805417680365

The Correlation Coefficient of Days From Cut-Off and Reading Scores = -0.235007606738772
My hypothesis that the further the student was born from the cut-off date the lower acheivement scores turned out to be true but it is not very significant. There is a negative correlation that shows the longer the days the lower the score is correlated but judging by the graph there is a lot of variance. When the trend line is added in it shows a bit of a downhill slide, but not too much.
Days From Cut-off
Math Achievement Score
Reading Achievement Score
1
470
480
229
433
432
236
445
434
9
436
441
9
430
440
6
434
446
48
420
439
5
456
462
209
441
442
210
456
468
31
432
428
26
430
435
226
453
448
125
430
424
70
452
459
93
442
446
234
437
434
131
439
442
279
426
435
67
443
447
40
447
442
36
451
457
282
457
450
43
425
427
46
449
451
140
420
425
299
442
451
14
446
453
34
446
453
233
426
427
101
434
424
266
448
437
154
453
432
11
454
451
104
429
424
42
446
450
31
449
453
17
453
462
11
449
445
62
450
436
186
452
468
170
446
439
6
456
448
50
458
462
83
446
453
172
447
450
240
439
438
434
424
440
91
429
430
84
427
442
122
445
443
142
451
435
104
457
462
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