The Organisation for Economic Co-operation and Development (OECD) monitors math, reading, and science performance of high school students in 64 countries using standardized scores. The scores for 10 selected countries at the top of the rankings in 2012 are given in the following table:

Investigate the relationship among math, reading, and science performance as follows:

a) Draw scatterplots between pairs of variables (three graphs). Comment on whether these graphs indicate that it’s appropriate to calculate correlation coefficients.

b) Calculate a 3 × 3 correlation matrix giving the correlation between pairs of variables.

c) Interpret the meaning of the diagonal terms in the matrix from (b).

d) Comment on whether there is any relationship among math, reading, and science performance in the 10 selected countries.

e) Does this data indicate any relationship among math, reading, and science performance in all 64 countries?

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Math Reading Science Shanghai-China 613 570 580 Singapore 573 542 551 Hong Kong-China 561 545 555 Chinese Taipei 560 523 523 554 536 538 Korea Macao-China 538 509 521 Japan 536 538 547 535 516 525 Liechtenstein Switzerland 531 509 515 Netherlands 523 511 522 Estonia 521 516 541 Finland 519 524 545 525 Canada 518 523 Poland 518 518 526 Belgium 515 509 505 Germany 514 508 524