Question

Is the math SAT score correlated with verbal SAT scores? J. What would you predict the...

  1. Is the math SAT score correlated with verbal SAT scores?

J. What would you predict the math SAT score would be for a state which has a verbal SAT score of 510?

STATE Mean SAT I Verbal Mean  SAT I Math
New York 497 510
Connecticut 515 515
Massachusetts 518 523
New Jersey 501 514
New Hampshire 522 521
D.C. 489 476
Maine 505 501
Pennsylvania 501 502
Delaware 500 499
Georgia 494 493
Rhode Island 503 502
Virginia 515 509
North Carolina 499 507
Maryland 511 515
Florida 499 499
Vermont 516 512
Indiana 501 506
South Carolina 491 495
Hawaii 487 514
Oregon 527 528
Alaska 518 514
Texas 493 499
Washington 528 531
California 501 519
Nevada 507 514
Arizona 523 524
Montana 537 539
Ohio 538 542
Colorado 554 553
Idaho 540 539
West Virginia 524 514
Tennessee 567 557
New Mexico 554 543
Kentucky 559 557
Wyoming 551 546
Michigan 563 573
Illinois 585 597
Minnesota 587 593
Alabama 560 553
Kansas 584 585
Louisiana 564 561
Missouri 587 585
Nebraska 569 576
Oklahoma 569 566
Wisconsin 587 596
Utah 565 556
Arkansas 569 555
Iowa 593 602
South Dakota 594 597
Mississippi 562 547
North Dakota 582 601
Math   Statistics-And-Probability   
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Answer #1
ΣX ΣY Σ(x-x̅)² Σ(y-ȳ)² Σ(x-x̅)(y-ȳ)
total sum 27305.00 27375.00 57278.16 57397.18 55536.71
mean 535.39 536.76 SSxx SSyy SSxy

correlation coefficient ,    r = SSxy/√(SSx.SSy) =   0.96859

Ho:   ρ = 0  
Ha:   ρ ╪ 0  
n=   51  
alpha,α =    0.05  
correlation , r=   0.9686  
t-test statistic = r*√(n-2)/√(1-r²) =        27.2667
DF=n-2 =   49  
p-value =    0.0000  
Decison:   p value < α , So, Reject Ho  
the math SAT score is correlated with verbal SAT scores

==================

Predicted Y at X=   510   is          
Ŷ=   17.65029   +   0.96960   *510=   512.145

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